The American joined the Trotters in January 2012 and he has endured a turbulent introduction to the English game having struggled for regular football since his arrival and suffering relegation from the Premier League.
Ream had been linked with a move to Championship rivals Middlesbrough, but agent Patrick McCabe denied the rumour, saying the 25-year old is prepared to stay put.
"The Middlesbrough thing took me aback a little bit," he told The Bolton News.
"If they have made an enquiry then they have done so to the club and not to me. Tim has very much liked being in Bolton. He is settled.
"Sure, he probably hasn't seen as much game time as he would have liked, but my impression is that he is looking forward to getting back into pre-season training and working hard to change that. He's hoping for a fresh start."