The attacker has been the source of speculation this past week after it was reported he was looking to leave Parkhead with Brighton and Bournemouth said to be favourites for his signature.
Sinclair is the reigning Scotland PFA Player of the Year but has failed to match his performances from last season in the current campaign.
He has found himself starting games on the bench in recent weeks and didn’t even play a single minute of the 3-2 victory at Ibrox earlier in the month.
Despite this, Rodgers insists Sinclair is fully committed and not looking to go anywhere at this point in time.
He said: “I saw some stuff over the international break. People have to fill pages and write headlines. Scott is very happy here. Of course he hasn’t played in the last few games because we changed the tactical ideas of the team.
“This is a period of the season now that he loves. He is a really competitive player and he turns it on in the big games.
“He is still very important to what we do. I wouldn’t be surprised if there is interest in him. He has scored more than 40 goals since he has been here over the two seasons and if you can do that as well as create all the assists that he does then he is always going to create an interest.
“He has had experiences that makes him appreciate what he has here. He is on a nice little break and he looked very good this week in training. He is here for the run-in.”