According to The Daily Telegraph, the Labour leader was investigated over fears he could have been a threat to national security.
The investigation was launched, the paper claims, at a time when Mr Corbyn, then an outspoken Labour backbencher, was supporting convicted terrorists and campaigning for a unified Ireland.
According to the paper, he supported one of the Balcombe Street gang, which waged a 14-month bombing campaign, and also had links to a bombmaker believed to have been behind the Hyde Park and Regents Park attacks.
Mr Corbyn also shared a platform with a wanted IRA killer, the Telegraph claims, and John McDonnell once claimed that the pair of them used to “pin people against the wall” in the Commons to lobby them on behalf of Ireland.
Responding to the Telegraph’s claims, a spokesman for Mr Corbyn said: “MI5 kept files on many peace and Labour movement campaigners at the time, including anti-Apartheid activists and trade unionists.
“Jeremy campaigned for peace in Northern Ireland. To do so, he campaigned for the rights of all to be respected and spoke to people on all sides of the conflict.
“Jeremy campaigned for fair trials and against miscarriages of justice, after a series of well-publicised cases, such as the Guildford Four and the Birmingham Six.”
The spokesman added: “John and Jeremy do not pin people to walls. This is clearly figurative language.”
The Telegraph says it was against the background of his support for the Republican cause that MI5 began looking into Mr Corbyn’s activities. A source close told the paper a file was opened on him by the early 1990s.
The source told the Telegraph: “If there was a file on someone, it meant they had come to notice. We opened a temporary file and did a preliminary investigation. It was then decided whether we should open a permanent file on them.”
A file would be opened on “someone who sympathises with a certain group, or is friends with a specific person” and the purpose was to “assess whether the person was a threat”, the source added.
The Metropolitan Police’s Special Branch was also monitoring the Labour leader at around the same time, but it is unclear if the intelligence was shared, the Telegraph reports.
The paper says Peter Francis, an undercover officer turned whistleblower, has revealed that the force secretly compiled files on Mr Corbyn and nine other MPs which detailed their political beliefs, personal background and any demonstrations that they attended.
He was personally asked to collect information on the Islington North MP as he infiltrated anti-racist groups in the 1990s, he said.
Conservative peer Lord Tebbit told the Telegraph: “I think it just marks him out as what he clearly is: a hard-Left, Marxist, terrorist sympathiser.
“It leaves him very comfortable in the company of McDonnell, who, as we know, said that they will gain power not through Parliament but on the streets and the picket lines.”
The former Tory chairman, whose wife Margaret was left permanently disabled by the 1984 bombing of the Brighton’s Grand Hotel, added: “It’s a comfort to know that they were indeed being monitored, although clearly they stayed just on the right side, for them, of being charged with any offences.
“It just makes me feel that Mrs May is being perhaps unnecessarily indulgent towards the Labour party in order to win this election.”
It is also claimed that the London Labour Briefing, a magazine which Mr Corbyn sat on the board of and frequently contributed to along with Mr McDonnell and Diane Abbott, was being monitored by the security services.
One reader purporting to be an MI5 worker wrote to the magazine on its 25th anniversary claiming that it has been their job for 25 years to monitor the publication.
At the height of the Troubles, Mr Corbyn was a regular face at Republican protest events and attended events honouring dead terrorists, the Telegraph reports.
On one occasion it was reported in a Sinn Fein newspaper that he shared a platform with an IRA volunteer who was wanted over the killing of an SAS soldier and whose extradition had been requested by the British Government.
The Telegraph says that at another event commemorating Bloody Sunday, Mr McDonnell boasted that in the Lobby of the House of Commons he and Mr Corbyn had “pinned people up against the wall and said ‘do you know what has happened in Ireland in your name?'”.
As well as attending protests, the Telegraph says that in 1987 Mr Corbyn handed a petition to then-prime minister Margaret Thatcher demanding better visiting conditions for Hugh Doherty, a member of the Balcombe Street gang serving 11 life sentences, and fellow IRA prisoner Nat Vella and calling for “the immediate transfer of Irish political prisoners to prisons near their homes”.
The paper says archives from Troops Out, a London-based Republican organisation backed by Mr Corbyn, show him supporting the cause of Dessie Ellis, who was sentenced to 10 years in prison on explosives charges in the 1980s.
Ellis, whose family Mr Corbyn spoke alongside, was convicted of possessing bomb-making parts suspected of being used for the Hyde Park and Regent’s Park attacks.
The Telegraph also reports that Mr Corbyn toured Ireland in the 1990s addressing rallies calling for withdrawal of the British.
And it claims archives show that fellow MPs and members of his own party were “appalled” at his decisions to invite Irish Republicans into the Houses of Parliament soon after the Brighton bombing.
The Telegraph reports that Mr Corbyn was visited in the Commons by Gerard McLochlainn, the former “voice of Sinn Fein in London”, who had recently been released from prison for conspiracy to detonate explosives, and Linda Quigley, who had also been recently released from a sentence for IRA-related offences.
The pair attended just weeks after Mrs Thatcher was targeted in the Brighton bombing, which killed five people, including the Conservative MP Sir Anthony Berry, the paper says.
The paper also refers to a Sunday Times report last weekend that Mr Corbyn was arrested in 1986 for joining a protest outside the Old Bailey to “show solidarity” with terrorists including the Patrick Magee, who was later convicted of the Brighton bombing.
:: And don’t forget to watch it on Sky News: The Battle For Number 10 on Bank Holiday Monday, 29 May, at 8.30pm.