The midfielder, who was offered a one year deal by City with wages nearly three quarters less than what he was on last season, will train with The Reds in a bid to win a contract.
"He is a good solid player with good experience and, with the average age of the squad as young it is, it is important we have one or two who have been there, seen it and done it," said Forest boss Colin Calderwood to his club's website.
"We know what Stephen is all about, so it's just an invitation for him to get started with pre-season training and have a look at where we all stand.
"It is not just an open invitation for him to come here and get fit. He has come here so we can assess him and give him the chance to put himself to the forefront of our minds.
"We all know where we stand. There were other clubs that offered him the same opportunity so I am delighted that he has chosen to come here."