Lingard is rumoured to be looking for a move away from Old Trafford as he enters into the final year of his current contract with the Premier League side.
The England international spent the second half of last season on loan at West Ham but the Hammers are struggling to secure a permanent deal for the 28-year-old.
According to reports from the Daily Mail, Atletico have now registered an interest in him, as he prepares for key talks with Ole Gunnar Solskjaer this month.
United want to retain him on a new contract, but Lingard is unconvinced of his first team role under Solskjaer, and could move on if an acceptable offer is received.
West Ham are prepared to offer £20m for the United academy graduate but Atletico will aim for a lower fee due to his anticipated contract demands.