The 30-year-old helped Atleti lift the La Liga title this past season.
But a return to England is appealing for Trippier, especially in the north west where his family resides.
Atleti want £20m for Trippier, but the BBC reports United are unhappy with the valuation.
Given the former Tottenham man has just one year remaining in his current contract, the Red Devils feel they should part with a smaller fee.
Ole Gunnar Solskjaer is enamoured with Trippier's versatility and the fact he will provide competition for young right-back Aaron Wan-Bissaka.