Ferguson, who scored 66 goals for Dunfermline in 89 league appearances between 1964 and 1967, was inducted into the club's Hall of Fame in 2007, and learned of their desperate plight last month after a visit from his former Pars team mate Roy Barry.
The match with United is planned to take place at Dunfermline's East End Park ground in the summer, presuming Dunfermline ride out their immediate financial problems.
Barry told a "Save Our Club" public meeting on Monday night: "I went down a few weeks ago to see Man United and Everton play and I finished up getting quite drunk with Sir Alex, as normally happens when we meet.
"We were having a chat about the problems up here and I said: "What can you do to help Dunfermline?"
"Sir Alex said: 'I tell you what I will do, I will send a strong team up there and that will raise you a few quid.' I just looked at him and I couldn't believe him for a minute."
Dunfermline, formed in 1885, expect to be issued with a winding up order by Britain's tax authorities for an unpaid bill of £134,000 on Friday.
Local rivals Raith Rovers and Cowdenbeath are also trying to help Dunfermline survive with a statement on Raith's website reading: "Dunfermline Athletic are, and hopefully always will be, our fiercest sporting rivals ... but they are also our friends, and we would like to offer our friends a helping hand in their hour of need."
Raith, who host Dunfermline in a First Division match on Saturday, have said that for every supporter over 2,000 in the visitors end, they would donate that money to Dunfermline.
Dunfermline, Scottish Cup winners in 1961 and 1968 and semi-finalists in the old European Cup Winners Cup in 1969, are currently fourth in the first division, but with no realistic hope of gaining promotion to the Premier League this season.