The striker is currently at Old Trafford on a temporary deal from Monaco, with United able to make his stay permanent if they cough up £40m.
However, Falcao's poor form and lack of fitness has left Louis van Gaal unimpressed, and he will return to France once his loan expires.
Monaco have already revealed that they have had a number of enquiries for the Colombia international, and reports in Spain claim that Valencia are leading the race for his signature.
Radamel Falcao Player Profile
The La Liga outfit are pushing hard for a top four finish, but owner Peter Lim is determined to see the club challenge Real Madrid, Barcelona and Atletico Madrid for next season's title.
Valencia already have a number of strikers on the books, including Manchester City loanee Alvaro Negredo and starlet Paco Alcacer, but are desperate to bring Falcao to the Mestalla.
The former Porto hitman would be a major coup for Els Taronges, and could rediscover his confidence back in Spain after becoming a world star during his time with Atletico.
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