Angel Di Maria helped Real win the Champions League last season and scored Argentina’s extra time winner against Switzerland at the World Cup on Tuesday.
But talks about a new, improved contract for the 26-year-old have stalled amid claims in Madrid he is being too greedy, and Real have decided to test the market for him.
United have been keeping tabs on Di Maria but value him at closer to £30m.
He is understood to have reservations about joining a club who will not be playing Champions League football next season though.
“Sources at Real insist a deal can be done and super-agent Jorge Mendes is working to make it happen”
But sources at Real insist a deal can be done and super-agent Jorge Mendes is working to make it happen.
Arsenal, Paris St-Germain and Juventus have also expressed an interest in Di Maria but United are understood to be at the head of the queue.
Real hope to use the money from his sale to fund a bid for Colombia star James Rodriguez of Monaco, another player in the Mendes stable.
United have already brought in Luke Shaw and Ander Herrera this summer in deals worth a combined £60m.
But signing Di Maria would be an even bigger statement of intent for new boss Louis van Gaal.