The two clubs are already locked in negotiations for David de Gea, who is thought to be closing in on a switch to the La Liga giants.
And when the two sides officially sit down to finalise a potential move, Old Trafford transfer boss Ed Woodward will raise the subject of Bale and Benzema.
The pair are key members of Los Blancos’ attacking line, even though both have been criticised by Bernabeu supporters in the past.
Real are unlikely to be open to the idea of offloading both, but United have shown in the recent past that they’re willing to splash the cash to get the names they want.
The Madrid outfit are facing an uncertain few months, with imminent managerial arrival, Rafa Benitez, likely to impose his own style on the squad.