Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
Warnock is set to play the final game of his three-month loan spell from Aston Villa when Wanderers take on Peterborough this weekend.
Freedman confirmed Warnock is due back at Villa Park after the London Road clash but is open to the 31-year-old returning in the new year.
"The ball is firmly in Stephen's court and if he expresses any interest in staying then we will certainly look at it," Freedman told Bolton's official website.
"Until that time we are kind of snookered. He is a loaned player and he will go back to Villa after Saturday.
"Stephen has done fantastically well for us, we feel that in and around the place, and on the pitch, that he has been fantastic and we would like to look at that situation if Stephen would.
"We have said to Stephen that he needs to be comfortable with his decision, see if he has enjoyed it and he will go away and think about it over the next couple of weeks.
"I am sure he will have a nice Christmas and he will let us know how he is feeling in January.
"If he tells us that it is all positive then we will go to the board and try to explain why we should do something."