Martinez, who joined the Red Devils from Ajax back in 2022, has gone on to make over 100 appearances for the club, with several injury setbacks impacting his time in Manchester.
The Argentina international has endured a controversial few weeks after slamming United's hierarchy, including director of football Jason Wilcox, following their UEFA Champions League defeat to Atletico Madrid.
He later apologised, and has returned to Michael Carrick's squad plans, but his time at the club may over.
United could be open to January offers - to avoid losing him for free - but Atletico and Barcelona are happy to wait according to Spanish outlet Diario AS.
Atletico brought in his Argentina centre-back partner Cristian Romero in August and Martinez may prefer a Madrid link up over a battle to start in Catalonia.