The former Tottenham, Manchester United and Fulham forward has been without a club since leaving Greek side PAOK in June
But the 35-year-old has expressed an interest in returning to the Premier League and Bradley has forwarded his name to the Swansea hierarchy
Berbatov told BBC Radio 5 live Sport on Wednesday night: "When you've played in the Premier League you don't want to play anywhere else
"In this stage of my career I know where I am - I would happily play for a team where they use my experience and my knowledge.
"I can help young players develop and make the team stronger.
"In the end it's all about helping the team play."
Bradley believes Berbatov, who scored over 120 goals in English football and won the Premier League twice at Manchester United, could help Swansea escape the relegation zone
And the former United States boss revealed that the striker's name has already been spoken about regarding recruitment
"'I actually saw him (Berbatov) in May at the celebration game for Hristo Stoichkov in Sofia," Bradley said at his press conference ahead of Sunday's home game against Manchester United
"So I have met Dimitar a few times and I know he is anxious to get back into the Premier League.
"Everyone inside our club knows that, and so when there are (transfer) discussions his name is included.
"Where it takes us at this time I don't have an answer.
"But certainly I know about his intentions and I have certainly seen some of the good things he's done in the past.
"Yes he's on my radar - there's a lot of things on my radar right now.''
Bradley's opposite number on Sunday, Jose Mourinho, will spend the match in the stands after being given a one-game touchline ban on Wednesday.
Mourinho accepted two Football Association misconduct charges in relation to comments made about referee Anthony Taylor prior to the draw with Liverpool, and for using abusive/and or insulting words towards a match official during Saturday's game with Burnley.
The Portuguese, who was also fined a total of Â£58,000, was sent to the stands by referee Mark Clattenburg in the goalless draw against Burnley.
"Whenever you get into these situations with the authorities it is hard to know sometimes what is right and what is wrong," Bradley said.
"I don't have a good enough feel for precedent, normally decisions get made based on other things that have happened in the past.
"I am a football manager so I tend to side with football managers in these kind of situations.
"But all of us have to deal with the fact that somewhere along the line you have to be smart about what you say and what you don't say.
"After the fact it might feel good sometimes to get it out but usually it doesn't change anything.
"I have not seen too many calls after the match that get reversed.
"It's part of what you deal with
It's easy after every game to look at all the things that did not go in your favour."
Source : PA