The 21-year-old Welsh international has been one of the standout performers for Brendan Rodgers' side this season, and last week reports suggested he had also attracted interest from Liverpool.
The Swans are keen to keep hold of Allen, particularly at this stage of the season, and would demand a fee in excess of £10million for a player who is under contract until 2015.
Reds boss Kenny Dalglish is also believed to be monitoring the situation closely as he plans a summer move for the talented youngster, having sent scouts to the Liberty Stadium on a number of occasions already this season.
Allen has earned rave reviews for his sensible use of the ball, helping teammate Leon Britton be ranked among Europe's leading passers in 2011-12 - beating the likes of Barcelona duo Xavi and Andreas Iniesta.
The talented midfielder fits the model of young player that Liverpool director of football Damien Comolli wants to bring to Anfield, but interest from Tottenham could now thwart their plans to sign the Swansea star.