Lingard has shone at the London Stadium since joining on loan for the remainder of the season in late January.
West Ham are desperate to sign Lingard, with the 28-year-old scoring eight goals and providing three assists in his nine Premier League matches for the Hammers.
Reports last week claimed United were open to selling Lingard and Ole Gunnar Solskjaer was prepared to use the England playmaker in negotiations to sign Hammers star Rice.
Rice is valued at close to £100m but United’s asking price of around £30m for Lingard could see any deal come down to between £65m-£70m.
But ESPN report that Lingard’s representatives have poured cold water on any attempts from his parent club to use him in a deal to sign Rice.
Lingard is yet to make a decision on his future but he’s attracting interest from all across Europe, with Real Madrid, Paris Saint-Germain and Inter Milan said to be interested.
The 28-year-old wants to play Champions League football next term, with West Ham currently fourth in the Premier League.
But he wants a decision on his future to be his own and will not allow United to use him in a part-exchange to sign Rice.
Lingard hasn’t ruled out returning to Old Trafford and United could even offer him a new deal to protect his value.
The midfielder’s current contract expires in 2022.