Greek forward Samaras and Welsh midfielder Ledley are both out of contract at the end of the season but Lawwell insists the club is desperate to retain the services of the pair.
"We're talking to the representatives of both players. We'll be doing that over the next few weeks," he told Sky Sports News.
"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 (January) 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."
For the big stories and the banter follow us on Twitter: @tribalfootball