Stefan Johansen has just 12 months remaining on his contract at Celtic.
Johansen has just 12 months remaining on his current Celtic deal, and he is yet to agree a deal with the Glasgow club.
Galatasaray have shown an interest in signing the central-midfielder, but Rodgers is keen to keep the Norwegian at the club.
The former Liverpool boss says that Johansen’s performances in training have caught his eye, but he would understand if Celtic did opt to accept a bid for the 25-year-old.
“You could see with his performance he was keen to play. I can see his qualities and he’s working hard in training,” Rodgers said.
“This is a really volatile period for players and it’s only when the window shuts down that you get certainty and stability.
“The club has to protect itself. If a player clearly doesn’t want to be at a club and has a year to go, the market will tell you that you have to sell that player.
“There are very few players who will be allowed to run their contract through to a free. That doesn’t make any sense.
“We’ll see what happens. It is speculation but he is a player I’d like to keep for sure.”
Johansen was one of Celtic’s most integral players during the 2014/15 campaign, but his form last season badly dropped off.
Johansen was well short of his best during the previous campaign, but he remained a fairly important part of Ronny Deila’s starting line-up.
Whether Rodgers intends to give Johansen a starting role remains to be seen, but he has shown glimpses of quality of pre-season.
Celtic’s first competitive match of the new campaign comes next week, when they will take on Lincoln Red Imps of Gibraltar in Champions League qualification.