Despite agreeing not to raid his former club new it’s emerged that Brendan Rodgers is keen to bring the 22-year-old to Anfield in order to bolster his midfield options ahead of the new season.
Rodgers has yet to sign a player since taking over from Kenny Dalglish and had looked odds on to sign former Swans loan star Gylfi Sigurdsson before he signed for Tottenham Hotspur.
£10million-rated Allen blossomed during his debut campaign in the Premier League and was chosen to represent Team GB at the 2012 Olympics next month.
And Laudrip has played down talk of a switch to Merseyside insisting that he remains a major part of his plans as he prepares for his first season managing in England.
“I want Joe to stay here because he is very important for the team. As far as I know, we have heard nothing from Liverpool,” said the new Swans boss.
“If it is more than just rumours then I’m sure the chairman will talk to me about it.”
That admission is unlikely to deter Rodgers who gave Allen his chance to shine in the Championship and aided his development in the top-flight that saw him become ones Swansea’s stand-out performers last term.
The Northern Irishman has intensified his search for new players in the last week and is hoping to conclude a deal for Roma striker Fabio Borini before jetting off on the pre-season tour of North America.
The Serie A club confirmed Liverpool are chasing the 21-year-old Italy international interest on Wednesday with discussions being held over a £10m move.
“There is a real interest shown by Liverpool for Borini,” sporting director Walter Sabatini said. “We are evaluating the situation with (Roma general manager) Franco (Baldini).”