Berbatov's agent Emil Dantchev has confirmed his player is unhappy at Craven Cottage, and with just over six months left on his Fulham contract, would be open to moving next month.
Liverpool were linked with the Bulgarian forward under Kenny Dalglish, but a move collapsed after the Anfield legend left and Berbatov eventually moved to west London.
Reds boss Brendan Rodgers is expected to be active in the January window as he looks to build upon the club's impressive start to the season. And a striker could be a priority - earlier this week Liverpool were linked with Burnley forward Danny Ings following injury to first-choice Danny Sturridge.
The report notes Arsenal are also on the lookout for a striker to compliment Olivier Giroud. The Frenchman has led the line well for the Gunners, but Arsene Wenger fears a long-term injury to Giroud could severely dent Arsenal's title aspirations.
And Dantchev's recent comments could open the door for the Premier League duo.
"I don't usually speculate as nobody knows what will happen in January but what I can tell you is he [Berbatov] is not happy at Fulham," he said.
"He would like, if possible, to find another option. I cannot comment [on whether there has been any approach] but the priority is to find a solution to stay in England."