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Valencia has played only eight times in all competitions this season thanks to a combination of injury and competition, and will leave on a free transfer at the campaign's end.
The Ecuadorian has spent almost a decade at Old Trafford after joining from Wigan for £16 million in 2009, playing 338 times for the Red Devils and winning six major trophies en route.
But with Diogo Dalot breaking through this season and Ashley Young preferred at right-back, Valencia has fallen further down the pecking order.
Ads a result, his father Luis told El Universal: "He definitely will not continue in Manchester.
"He wants a change in the air and the club is not going to renew [his contract] either. Like everything in life, everything comes to an end.
"Arsenal, West Ham, Inter Milan and one club from China are options, but in football everything is changing.
"He wants to choose the best option, but above all he wants to sign a contract for two years.
"Not for the money but for peace and hopefully, he told me, be hired by a team that fights for important things."
(Hold the Arsenal jokes.)
Hector Bellerin was ruled out for the season in January, although Unai Emery will expect to have the Spaniard back for the beginning of next season.
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