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.
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."
Lawwell was also keen to point out Swedish defender Mikael Lustig is in the frame for a new contract but talks over an extention to Kris Commons' deal can wait until a later date.
"We haven't done anything on Kris," Lawwell said. "He has a year-and-a-half
to go and I think he is quite happy with that.
"Mikael has a year-and-a-half to go and we are hoping to start conversations
with his people as well. He has been fantastic, a great buy, a great find, and
he has done really well for us."