The forward has been without a club since being released by Greek side PAOK in June.
He has been vocal about a return to the Premier League, after speaking with BBC Radio 5 Live about the subject.
What did Bradley say?
“I have met Dimitar a few times and I know he is anxious to get back into the Premier League,” Bradley said.
“Everyone in our club knows that and so when there are discussions, his name is included.”
Bradley continued to note that these sort of moves take time and that he doesn’t have an answer [to whether the deal will go through] but Bradley is aware of the striker’s intentions.
Does Berbatov want the move?
The Bulgarian also had spells with Fulham and Monaco before his move to PAOK, where he spent the 2015-16 campaign.
Berbatov admitted that once "you've played in the Premier League" you don't want to play anywhere else
He has also been linked with a move to Sunderland, the only side below Swansea in the table.
Where would Berbatov fit in the side?
While Swansea have scored just nine Premier League goals this season, the 16th lowest of any side, the problem doesn’t seem to be with the strikers.
Fernando Llorente looks promising, despite having just one Premier League goal to his name. Borja Baston also has shown a lot of good qualities and is finally fully fit.
A move for Berbatov would also surely crush young striker Oliver McBurnie’s confidence. The Scot scored twice in the EFL Cup win over Peterbrough and impressed in pre-season and for the under-23 squad.
In the past, Swansea have been linked with seasoned veteran players such as Rafael van der Vaart and Real Madrid legend Raul, but the club has dismissed them, as those sort of moves didn’t align with the club’s ethos.
However, ‘The Swansea Way’ has been gradually reduced to a memory over the past couple of seasons, and the sale of the club seems to have cemented that.
Three years ago, a move like this would seem ridiculous as it wouldn’t make sense. Swansea of present day are without an identity, and a move for Berbatov would reflect that.