Benzema was top of Fergie's wish-list for a new striker a few months ago, but he was given no encouragement by Lyon, who are notoriously hard to deal with.
However, Fergie has now decided to make an offer which could go as high as £30m.
Ferguson knows Benzema is one of the few players who could make a difference and help take his side to the next level.
United insiders say Fergie and Gill are 'working on something big', but have also set a deadline to tie up the move. Ferguson hopes to move fast because he knows the price could rise if Benzema has a successful Euro 2008.