The 29-year-old, who joined the Reds on transfer deadline day last September, had a tough time at Old Trafford, scoring just four goals in 29 appearances.
“Falcao is a top professional and a good human being. On behalf of myself and everyone at the club I would like to wish him well for the future,” United’s coach Louis van Gaal told the club’s official website.
United won a hotly-contested race to sign the Colombia striker on loan from Monaco last close season, as La Liga giants Real Madrid seemed poised to attract the former Porto and Atletico Madrid forward.
Manchester had the chance to sign him on a permanent basis for £43.2million, but the club have told Falcao they will not exercise that option.
Falcao was even left out of United’s squad for the final game of the season at Hull on Sunday through injury, according to Van Gaal.
‘El Tigre’, as he is known to Colombian fans, may not stay for long in the Principality as the striker has been reportedly linked with moves to Chelsea, who are looking to replace Didier Drogba, or his former club Atletico, who could lose forward Mario Mandzukic.
Falcao missed last year’s World Cup with a knee injury.