Publication of the review, carried out by Sir Desmond de Silva, will be marked by a statement in the House of Commons from Prime Minister David Cameron. The investigation runs to 500 pages and will be published later this month.
Father-of-three Mr Finucane was shot dead when loyalist UDA/UFF gunmen used sledgehammers to burst through the front door of his home in north Belfast in February 1989.
Mr Cameron has accepted that collusion took place and apologised to the Finucane family.
A letter from Sir Desmond to Mr Adams said: "Whilst the focus of my report is Patrick Finucane's murder, it was appropriate for me to examine it in its proper context. Among the surrounding key issues is the role played by the British Army agent Brian Nelson.
"Accordingly, I wanted to make you aware prior to publication that my report touches on the plot by loyalist paramilitaries to attack you in May 1987."
Mr Adams said: "Collusion between British state forces and unionist death squads was a matter of institutional practise by successive British governments throughout the decades of conflict in the north.
"It played a part in the attack in March 1984 in which I and three others were shot and it has already been reported that the British were aware of the plan to kill me in May 1987."
Mr Finucane's widow Geraldine and relatives have been critical of the £1.5 million review ordered by the Prime Minister, claiming it falls short of the full public inquiry they demanded.
As well as the 500 page report, another 500 pages of supporting documentation will be published at the same time, on December 12. Sir Desmond has already said his report will include previously highly-classified material relating to the murder.