The Welsh international has just 12 months left on his current deal and is unlikely to extend it without assurances of regular first team football.
With the likes of Grujic, Henderson and Can already at the club, Klopp cannot make any such promises to the former Swansea player.
Liverpool Echo are now reporting that Stoke City have submitted a 13 million pounds bid for the Euro 2016 star and the Reds have accepted the offer.
The player is now expected begin talks with the Potters regarding his personal terms.
It is understood that Allen prefers a return to Swansea, but the Welsh club are yet to match Stoke’s offer/Reds’ valuation.