Khedira has also attracted interest from the likes of Chelsea and Arsenal, but United are looking to stump up high wages to secure the 28-year-old midfield enforcer, who becomes a free agent when his Real Madrid contract expires this summer.
With his contract almost up, the German international will make the choice of his next employer, with the Premier League looking his most likely destination, despite interest from Bundesliga club Wolfsburg.
He has made just eight appearances in La Liga this season and is part of one of the most competitive midfield groups in Europe.
Injury troubles have consistently hampered his career but Louis Van Gaal is believed to be keen on signing the powerful midfield man to add strength to the United midfield.
Van Gaal is expected to have another busy transfer window this summer and despite high wages, bringing in Khedira as a free agent could be a good start to a busy few months for the United manager.
The Dutchman also wants to sign German defender Mats Hummels and the Dortmund centre-back could link up with Khedira if both players move to Old Trafford in the coming months.
Would Sami Khedira be a good signing for Manchester United?