The Welshman is undergoing his medical this morning as part of his deal to re-join the Championship side.
It is understood that the midfielder will be signing a two-year deal to keep him with the Swans until 2024.
Allen is currently a free agent having had his contract with Stoke City expire following the end of last season.
The 32-year old was with the Potters since departing Liverpool in 2016.
But this will be Allen’s second stint with Swansea, having previously played for the club between 2007 to 2012, coming through the academy, before signing with the Reds alongside Brendan Rodgers.
The Welsh international enjoyed a successful first stint in South Wales, helping the team earn promotion under Rodgers in 2011.
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Allen was still a regular starter for Stoke up to last season, appearing in 41 league games for Michael O’Neill’s side, with 38 of those coming from the off.
But it is now looking inevitable that he will come back to the club where he started his playing career 15 years ago, as part of Russell Martin’s side.
This is a really solid signing for Swansea, especially considering the deal to sell Flynn Downes to West Ham.
His experience will be important, and his calm approach to possession should help deal with the tempo of any game.
Allen will be suited to Martin’s style of football and he showed last season that he is still more than capable of competing at a high level on a consistent basis.
The midfielder will also want to maintain a high level of fitness ahead of Wales’ World Cup campaign this winter, which Swansea should give him the platform to do so.