Real coach Carlo Ancelotti revealed yesterday that both midfielders could leave before the summer market shuts.
The Manchester Evening News says United boss Louis van Gaal may attempt to complete a double swoop for Khedira and Di Maria.
Madrid are understood to be willing to accept an offer lower than their previous £20m valuation for Khedira.
United executive vice-chairman Ed Woodward has already held talks with Madrid chiefs over a potential £50m deal for Di Maria.
For the big stories and the banter follow us on Twitter: @tribalfootball