The English attacker has excelled during a loan spell at West Ham United in the second half of this season.
Lingard is in the best form of his life, and has pushed West Ham into the top four of the Premier League.
According to Goal, Lingard has not decided on whether he wants to compete for a first team spot at United next season or secure a permanent move elsewhere.
West Ham do want to sign him permanently, while United would welcome him back as well.
The 28-year-old will be out of contract in the summer of 2022.