The 30-year-old has been linked with a move away from Los Blancos at the end of the campaign, having produced disappointing returns of only five goals in 19 appearances across all competitions this season - including just two in La Liga.
Spanish outlet Diario Gol now reports that Benzema is the latest player to be linked with Old Trafford, although some of their Premier League rivals have also been offered the chance to sign the Frenchman.
Tottenham and Arsenal are amongst those to be named in the report, while Italian champions Juventus are also thought to be on the list of potential destinations for the striker.
United boss Jose Mourinho ruled out any further attacking additions earlier this week, but Madrid are understood to favour a deal with the Red Devils due to their desire to take David de Gea in the opposite direction.
Benzema previously played under Mourinho at Real Madrid, where he has scored 186 goals in 389 appearances.