Liverpool were strongly linked with a bid earlier in the season, and could be alerted to comments made by Parma general director Luca Baraldi.
Parma would like to keep the French midfielder, but are prepared to dispense with his services if the price is right.
Baraldi said: "He's a very important player and it seems that many teams want him, but we haven't received any type of real offer.
"If he wants to leave, we won't stop him, but it has to be an offer bounded to his value and if this does arrive, we'll have to analyse it all together before making the decision."
Reds boss Gerard Houllier has seen his side`s title charge fall off the rails in recent weeks, and must be sorely tempted to raid the market in January.
Whether Lamouchi remains on his list of targets is not known, but the Frenchman would add a touch of class to the Anfield squad.
Internazionale coach Hector Cuper is also a fan of the midfielder, and is certain to monitor the developments closely.
A player certain to be on his way out of Parma is Sebastiano Siviglia, who seems set for a loan move to Atalanta.
Baraldi added: "Our only affair already done is the transfer of Sebastiano Siviglia to Atalanta."
On other moves, Baraldi added to Gazzetta di Parma: "Matteo Brighi will stay with us, and about this there won't be any other discussions.
"And Adriano too will stay. We spoke with Inter`s managers before last Sunday`s match and they've agreed that he'll have to stay here to grow because he needs to develop.
"He isn't yet a really great player. He has a lot to learn."
Parma are unlikely to make signings, with Baraldi adding: "Atalanta's Luciano Zauri? He's a player we've been looking at for a long time and that we would like to have here in Parma, but I think that until June he won't leave Bergamo.
"Simone Perrotta? We like him too, but at present there aren't the conditions to buy him because he costs too much.
"He could interest us if we could sell a few players. Certainly we'll look at him closely because we consider him a really good player."
