The 24-year old, who was picked in the USA's final World Cup squad, joined the English club in January but was restricted to just three appearances because of a broken leg.
However, that has not fazed manager Owen Coyle who is hoping to secure the former Houston Dynamo man.
"Like everyone, I have been really impressed with Stuart on and off the pitch since he came here," Coyle told the Bolton News. "The players really like him, and he's been terrific in each game he has played in for me.
"We had a meeting with his representative last week, and needless to say, I'd love him to be a part of this football club for a long time to come."