The investigation runs to 500 pages and will be published later this month.
Publication of the review, carried out by Desmond de Silva, will be marked by a statement in the House of Commons from British prime minister David Cameron.
Mr Finucane, a father of three, was shot dead when loyalist UDA/UFF gunmen used sledgehammers to burst through the front door of his home in north Belfast in Feb 1989. Mr Cameron has accepted collusion took place and apologised to the Finucane family.
A letter from Mr de Silva 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 the revelation came as no surprise. “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 Mar 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 £1.5m (€1.85m) review ordered by the prime minister, claiming it falls short of the full public inquiry they demanded.