Hibernian have vowed not to sell Kevin Thomson and Scott Brown during the January transfer window.
Hibs manager John Collins said the midfield pair could leave Easter Road in the summer, but would be staying in Edinburgh for the rest of the season.
Thomson has been stripped of the club captaincy and Brown had a transfer request rejected by the club.
Charlton had a £3m joint bid for the pair rejected in December. The Old Firm are also reported to be interested.
Both players signed long-term contracts with Hibs in March, but their agent Willie McKay then sought to renegotiate their terms.
But Hibs said they would not review their contracts and urged the players to concentrate on playing for the club.
"I'm very, very confident they'll still be here after the January transfer window"
Thomson, 23, is contracted to Hibs until 2010, while 21-year-old Brown signed a deal to keep him at Easter Road until 2009.
The Scottish Sun quoted both players on Monday as saying they would be interested in joining Celtic.
Collins said: "As I've said from day one, if you've got good football players there's always going to be speculation.
"We've never said they're for sale. They're on contracts with the football club and I just want them to continue to play football.
"I'm very, very confident they'll still be here after the January transfer window. It's me and my board of directors who make the decision."
Collins said Hibs had failed in their efforts to sign Falkirk's Alan Gow, after holding talks with the 24-year-old striker.
"Alan Gow won't happen, unfortunately," said Collins.
"We went about our business correctly, we contacted the football club and then spoke to the player and his agent and gave it our best shot, but it wasn't to be."