The United chief executive told 5 live that a new contract for top scorer Wayne Rooney would be on this summer's agenda, and confirmed that France striker Karim Benzema, then with Lyon, was on last summer's shopping list.
"We didn't get Benzema but we did offer 35m Euros," revealed David Gill. "(We made) just one phone call to the States (to United's owners, the Glazer family), saying we would like to make an offer of 35m Euros and they said 'fine'.
"We did it, but Benzema went to Real Madrid for something like over 40m Euros. Sir Alex has gone on record saying that was too much. But if I (again) went to Joel Glazer and said 'Alex wants a particular player, can we have the money?', the answer would be an unequivocal yes. They have demonstrated it.
"From my own personal perspective, we have no doubt that they (the Glazers) would support whatever we require.
"They will only get value back by ensuring the team continues to be successful, continues to attract exciting players