The right-back is out of contract this summer and will leave Old Trafford after falling out of favour under Ole Gunnar Solskjaer.
Valencia has struggled with injuries this season and has lost his place to fellow veteran Ashley Young.
The Ecuador hero’s dad, 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 him 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.”
The transfer revelation comes amid news that:
Arsenal have been forced to use midfielder Ainsley Maitland-Niles at right-back, with Hector Bellerin out with a long-term injury while Stephan Lichtsteiner has struggled when called upon.
But while the Gunners need cover in that position, fans have urged the club to look elsewhere.
“We can’t be that desperate surely?” said one supporter on Twitter.
While another added: “Nonsense!! Is he going to be a ball boy or what?? Arsenal is not interested in him.”
“Oh God I hope not he is finished maybe 5 years ago,” tweeted a third.
Comparisons have been drawn to Arsenal signing Mikael Silvestre from United in 2008.
The Frenchman struggled to impress at the Emirates and one fan doesn’t want his club making the same mistake.
They tweeted: “Awesome another washed up UTD defender. Embarrassing.”