Dembele, 20, enjoyed an extraordinary first season in Scottish football last term, scoring 32 goals as the Bhoys completed a clean sweep of the Scottish Premiership, Scottish Cup and Scottish League Cup.
The former Fulham striker was linked with a return to west London during the January transfer window amid reports suggesting Chelsea were to bid £34m (€38.8M) for his services. While nothing came of it, interest in the player from Stamford Bridge still active, according to the Evening Standard, with Arsenal and West Ham United also listing the Frenchman as a possible target.
Dembele missed the final weeks of the 2016-17 season with a hamstring injury, but returned with a goal in Celtic's 1-1 draw AGAINST Rapid Vienna on Saturday in a friendly.
Their campaign officially gets underway on 11 or 12 of July with a Champions League second-round qualifier against either Northern Ireland champions Linfield or San Marinese minnows La Fiorita.
Rodgers admits the club is bracing itself for offers for their prized striker, but insists no players will be leaving Parkhead until after their opening European match.
"Moussa is very content and happy," Rodgers said, the Scottish Sun reports. "He looks very fit and hasn't had a long lay-off. He went away with France Under-21s. He is someone of great character.
"He is very stable, nothing affects him. Of course he is not a player we want to sell.
"Like all the players we want to keep him, but we know how football works and we will see what happens.
"But certainly not until after the Champions League qualifiers, there won't be anything done before that. That goes for all the players."
Chelsea remain heavily linked with a move for Everton's Romelu Lukaku but should Michy Batshuayi leave the club this summer, there could be room for two new strikers. The Daily Record reported in June Antonio Conte will consider making Dembele his back-up striker should the Belgium international leave this summer.