Jurgen Klopp has recently placed his faith in Loris Karius but the Mirror claims the German believes England international Butland would represent an upgrade on his current options.
Earlier this week reports claimed Simon Mignolet had switched agents with a view to leaving Anfield at the end of the current campaign.
Stoke are resigned to losing their No.1 goalkeeper but believe they can attract a fee in advance of the world record £34.7million which brought Ederson to Manchester City from Benfica.
Butland is said to be aware of Arsenal’s interest but the prospect of working with Klopp is likely to heavily influence his decision.
More: Arsenal FC