Dembele enjoyed an impressive first season at Parkhead following his move from Fulham last summer and the 20-year-old has been linked with a string of leading clubs.
However, while Rodgers did not completely rule out the prospect of Dembele being sold in the transfer window, the Celtic boss insisted there will be no sudden departure for the forward.
“Moussa is very content and happy,” said Rodgers. “He looks very fit and hasn’t had a long lay-off because he went away with the French Under 21s.
“He is someone of great character. He is very stable, nothing affects him, but if there’s anything that comes in…
“He is not a player we want to sell, but we know how football works and we’ll see what happens.
“But certainly not until after the Champions League qualifiers, there won’t be anything done before then.
“That goes for all the players. I am very happy with the general make-up of the squad.”
Dembele missed the end of last season with a hamstring injury, but returned for Celtic on Saturday when scoring a penalty in a pre-season friendly draw with Rapid Vienna.
Celtic will face either La Fiorita or Linfield in the second round of Champions League qualifying, with the second leg of that tie taking place in the week commencing July 17.