The La Liga side had reportedly been interested in pursuing a deal for the 30-year-old this month, according to Marca, with his contract set to expire in the summer and no new contract yet to be offered by Manchester United.
However, the Spanish newspaper is now claiming that Valencia have ended their interest and will instead concentrate on a move for midfielder Saul Niguez, who currently plays for Spanish champions Atletico Madrid.
This latest development will come as good news to Premier League sides West Ham and West Brom, who have also been credited with an interest in the midfielder.
Both West Ham and West Brom bosses Sam Allardyce and Tony Pulis are rumoured to be looking for reinforcements during the January transfer window, with Allardyce in particular thought to believe that two or three signings could turn his team into regular top-six contenders.
Fletcher, now 30, currently has six months left on his contract at Old Trafford and the midfielder could make a difference for either West Ham or West Brom - although it remains to be seen whether the Manchester United man is past his best or not.