Hoops boss Neil Lennon is still determined to pull out all of the stops to keep the players at the club.
But he has made it clear that, unless they agree to new deals, they will be sold.
Lennon is bracedfor an intense four weeks of transfer activity, and is already showing signs of wearying at the number of players linked with the Parkhead club.
Wolves' Leigh Griffiths is the latest in a long line. But Lennon has dismissed this as "speculation" and refuses to discuss players under contract at other clubs.
While bringing in more quality remains his intention, his priority just now is to persuade Samaras and Ledley to commit to new contracts.
But, he warned: "If they don't reach negotiation, then we would be loathe to let them run their contracts out for nothing."
Lennon admits there is interest in Samaras.
Atletico Madrid are poised to test Celtic's resolve by offering around £1million for the 28-year-old, while Hull are ready to finally make their move for him if the La Liga club submit a bid.
But, Lennon insisted: "There's been no conversation between us and Hull.
"Sami is going to be vulnerable, and there's going to be a lot of interest in him because he's a quality player.
"But, we're not finished on our side of it with Sami."
Meanwhile, Crystal Palace continue to lead the chase for Ledley, though Lennon revealed the midfielder told him in a meeting on Hogmanay he wants to stay at Parkhead.
The manager said: "Hopefully, negotiations will start up again and we'll get that over the line this month."
Lennon does not know for sure what will happen next, but is adamant Celtic will not lose out financially.
He has already had the spine of one team he built ripped out, and is doing all in his power to prevent a repeat performance.
Lennon said: "At the minute, we are hoping to keep as many of our big players as we can."
The Hoops boss would prefer to be concentrating on adding more players, and will meet with newly-appointed scout, Peter Houston, tomorrow.
Lennon does not need to sell before he can buy, but a few players may be moved out - some on loan - during this window, for their own development.
Mo Bangura is set to re-join the squad after spending a year with Elfsborg, and Lennon confirmed: "Mo is due back tomorrow.
"He will not be coming to Turkey with us next week, but we will see him when we get back."
Tony Watt is on a winter break from Lierse in Belgium, but the future of the 20-year-old - who still has six months of his loan deal to run - has yet to be decided.