The Red Devils are expected to reignite their interest in the England international this summer, having missed out on a deal for the former Manchester City youngster last summer.
According to The Sun, Dortmund are interested in signing Lingard ahead of the 2021-22 campaign, and Man United could attempt to bring Sancho's asking price down by including the on-loan attacker in the deal.
The 28-year-old has been in excellent form for West Ham United since arriving at the London Stadium on loan in January, scoring nine times and registering four assists in 13 appearances.
The Hammers are said to be desperate to sign Lingard on a permanent deal but could be priced out of a move in the upcoming market.
Sancho, meanwhile, has again enjoyed an impressive campaign in Germany, and he scored twice and registered one assist as Dortmund beat RB Leipzig 4-1 in the DFB-Pokal final on Thursday.