The daily sports paper claim that the Lion’s were interested in signing the Ecuadorian international but were unable to match United’s demands.
The report goes onto state that Galatasaray were also after Rafael da Silva.
Valencia played at right-back for Manchester United last season however, the 30-year-old could see his first team opportunities limited following the arrival of Matteo Darmian from Torino.
The Ecuador international provided three assist in 35 appearances for Manchester United last season.
Galatasaray won the league title and cup double for the sixth time last season. The Lions lifted the Super Lig for a record 20th time and earned the right to add a fourth star to their crest.
The Istanbul giants booked a place in the Champions League group stages for the fourth consecutive season as a result of last seasons triumphs.
Galatasaray kick-off their league campaign this weekend against Sivasspor.