The 31-year-old has been linked with a move away from the Stadio Olimpico, having not featured for Rudi Garcia's side since November.
Premier League strugglers West Ham have been linked with the striker as Sam Allardyce looks to strengthen his attacking options ahead of a push for Premier League survival.
Borriello said goodbye to Roma fans on his official Twitter page on Friday, but left his potential destination out of the message.
"A salute to all the fans of Roma," he wrote. "These have been fantastic months, crowned by a wonderful record. Thank you all."
West Ham have been without record signing Andy Carroll for much of the season, although the England international recently returned to action after a lengthy injury lay-off.
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