Hodgson insisted: "We're not trying to get rid of Jimmy Bullard, but Jimmy Bullard is trying to get a contract which suits him.
"He's not sure we can provide that contract and, as a result, we have to be realistic and there might be clubs out there who can offer him that and who can match the transfer fee that we think he's worth. If it happens, it happens but he has not been told he can leave in January."
Bullard has been in strong form again this campaign, prompting a call-up to the England squad, and scored Fulham's only goal of their last four games in the 1-1 draw with Manchester City.
Hodgson maintains that he wants the former Wigan man to stay in January, but beyond that is uncertain.
Another player to irk Hodgson of late was right-back John Pantsil, who reacted theatrically after squaring up to Stoke's Ricardo Fuller.
"I didn't like it,'' said Hodgson. ''We have spoken about it and he knows how I feel.
"I think he regrets the situation, although he was the one who was knocked over. I didn't like the fact that he over-reacted to the push and I have told him so."
One goal and three goalless draws in the last four league games does not make for exciting reading but Hodgson said he was not worried and chose to look at that run as four games unbeaten.