The 21-year-old Wales international has impressed in the Swans' debut Barclays Premier League campaign, and has captured the attention of a number of rival suitors.
His sensible use of the ball has helped teammate Leon Britton be ranked among Europe's leading passers - beating the likes of Barcelona duo Xavi and Andreas Iniesta.
Reds boss Kenny Dalglish was first alerted to Allen's potential during Liverpool's 0-0 draw with Swansea at Anfield back in September, and has deployed scouts to the Liberty Stadium on a number of occasions to monitor his progress.
Allen fits the model of young player that Liverpool director of football Damien Comolli wants to sign – one who can be bought relatively inexpensively and whose value is likely to rise rather than decrease throughout the course of his contract.
However, a transfer during the January window looks to be unlikely, with Dalglish's priority signing a striker to strengthen his forward department this month.
Allen signed a new contract with Brendan Rodgers' side at the start of the 2011-12 campaign that ties him to Swansea, with whom he has been since the age of nine, until 2015.