The Ecuadorian is out of contract at the season and will be free to speak with foreign clubs next month.
According to The Sun, the Hammers want to bring Valencia to east London in the summer.
With Pablo Zabaleta expected to retire, manager Manuel Pellegrini wants to find another veteran to play at right-back.
Valencia has struggled for game and argued with Jose Mourinho this season, according to the report.
An Old Trafford source – via The Sun – said: “The club are still deciding what to do with Antonio and his future.
“He has played a few times this season, but has struggled with injuries and his form hasn’t been great.
“Him and Jose haven’t seen eye-to-eye at times this season and it might be the end for him here, but we will see.”