According to the Daily Star, after missing out on Inter Milan's Wesley Sneijder the Old Trafford manager will attempt to sign the precocious talent for a second time.
Fergie tried to sign the France international last summer following the sale of Cristiano Ronaldo, however like the Portugual winger, Benzema chose a switch to the Bernabeu.
New coach Jose Mourinho though has yet to decide on whether Benzema's future remains in Spain, as he continues to assess his squad ahead of the forthcoming season.
However, if the self-proclaimed 'Special One' decides he is willing to sell, Ferguson will move for his man before the transfer window closes at the end of next month.
The Old Trafford gaffer insisted last week he would not be making any more signings and is content with his current crop. Yet United's sources have confirmed that, ideally, Ferguson would like to add another attacking option to his squad.
The United chief already has Wayne Rooney, Dimitar Berbatov, Michael Owen, new signing Javier Hernandez and Federico Macheda at his disposal, but feels Benzema would be a welcome addition.
Benzema was largely disappointing during his first season in La Liga, where he scored just eight times in 27 matches and missed out on inclusion in the French World Cup 2010 squad.
He has also been involved in off-field scandals, but remains one of the most exciting and sought-after talents in Europe.
Meanwhile, United's other summer transfer target, Sneijder, has finally been persuaded to remain in Milan, despite having ambition to move to the Premier League.