The Southampton star was promoted back to the English top flight at the end of last season.
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However, he has not yet managed to agree a new deal with the Saints and has other offers.
Per The Sun, Torino and Wolves are among the teams ready to move in for Adams.
The 28-year-old is known to former Chelsea assistant manager Paolo Vanoli, who is now in charge at Torino.
Adams has been a free agent for the past two weeks and can speak to any club in the world.