Just 24 hours after reporting Anthony Stokes had signed a three-year deal, chief executive Peter Lawwell is looking to tie down another two key members of Neil Lennon's squad.
Fellow-striker Samaras, who scored his 50th league goal against Partick Thistle at the weekend, and former Cardiff midfielder Ledley are out of contract at the end of the season. The pair have been playing some of their best football and are a fair bet to remain at Celtic Park beyond the end of the current campaign.
Speaking to Sky Sports News, Lawwell said: "We're talking to the representatives of both players. We'll be doing that over the next few weeks.
"It's the first meeting we'll have with Georgios' representatives. We've been talking regularly to Joe's and hopefully we'll get something tied up before the end of December.
"Before the window opens, that's our objective, to have things clear before then.
"Ideally you'd like it done by then. Hopefully they stay and hopefully they commit themselves to Celtic.
"But if not, you need to make arrangements and that will be the right time to get clarity there."