The former Bulgaria captain, 35, is a free agent after being released by Greek club PAOK Salonika in June.
“Dimitar feels he can play for at least another year and his priority would be to come back to England,” Berbatov’s agent Emil Dantchev told BBC Sport.
Former Swansea boss Bob Bradley previously said Berbatov had been “on his radar”.
The former Tottenham and Fulham striker, who made 229 Premier League appearances over nine seasons, has previously been linked with a move to Major League Soccer.
He was part of the Manchester United squads that won the league title in 2009 and 2011, when he was joint Golden Boot winner with Carlos Tevez.
Berbatov was on the bench for the 2009 Champions League final defeat by Barcelona but missed out two years later when Sir Alex Ferguson’s side were beaten by the same opposition at Wembley.
In addition, he won League Cups with both United and Tottenham, scoring for Spurs in their 2-1 defeat of Chelsea in 2008.
