Allen, 22, was one of the stars of Swansea's impressive maiden Barclays Premier League campaign, with his form helping him secure a place in Stuart Pearce's Team GB squad for the Olympic Games.
The player signed a new four-year contract last summer but Rodgers is a keen admirer of the Wales international and reports have linked the Reds with a ?15million deal. But Press Association Sport understands there has been no contact from Liverpool, or any other club, over a possible move for Allen.
When Rodgers left for Anfield, Swansea insisted on a 12-month agreement preventing the Northern Irishman from stripping the club of their best players.
But it is understood if Swansea were to accept a bid from another club for a player, then Liverpool would be free to join the chase.
One man the Swans are hoping to bring in before Michael Laudrup's squad depart for their pre-season tour of the United States this weekend, is Rayo Vallecano midfielder Michu.
The 26-year-old midfielder, who scored 15 goals in the Primera Division last season, is set to hold talks over a 2million euro move to south Wales, according to reports in Spain.
Swansea say they have yet to receive notice from the financially stricken Spanish club that their offer has been accepted, but are optimistic that a deal can be completed.
Laudrup added defender Chico Flores and midfielder Jonathan de Guzman to his squad last week.
Source: PA
Source: PA