Liverpool boss Brendan Rodgers, who made the switch from the Liberty Stadium to Anfield to replace Kenny Dalglish this summer, confirmed his interest in the Wales international last week.
Allen signed a four-year deal with Swansea last year but Rodgers is keen to bring him to the north-west.
And the south Wales club are disappointed, claiming Liverpool agreed not to make approaches for Swans players until next year.
A club spokesman said: "Swansea can confirm that Liverpool have expressed an interest in Joe Allen, despite a written agreement with Liverpool not to approach any players within the 12-month period of former manager Brendan Rodgers leaving for Anfield."
The spokesman continued on www.swanseacity.net: "There has also been interest from other clubs regarding his possible availability and the club is due to speak to Joe, as originally planned, about the situation when he returns from GB (Olympic) duty.
"The club is not prepared to release any details on whether any formal bids have been made at this stage or details of Joe's contract, which are private and confidential.
"The club is extremely disappointed that speculation regarding certain aspects of his contract have been released to the media by parties outside the club."
Swansea, who finished three places and five points adrift of eighth-placed Liverpool in the Barclays Premier League, are keen to keep their current players.
The spokesman added: "Fortunately the club is in a financial position where it does not need to sell any of its players and will continue to work in the best interests of its supporters, who are our priority, and the club to provide new manager Michael Laudrup with the best opportunity to be successful in the forthcoming Premier League campaign."
Rodgers last week said: "I have a great relationship with Swansea but if there is a market for any of the players, I would like to be in that market.
"They respect that. He is a very talented player, which everyone knows but there is nothing more at the moment. When players come to a club such as Liverpool, it's never straightforward.
"There are always other barriers and difficulties. At this moment, there are ongoing negotiations on a few targets.
"We hope we're close to some deals. I need to evaluate the players we have and assess the squad and bring some in to bring freshness to the group.
"As a manager you want them in sooner rather than later but the main thing is to get them in before the beginning of the season. If we do that, our job will be done."