This is according to Catalan newspaper Sport, who believe Ter Stegen could be unhappy at the Camp Nou after failing to establish himself as Barça’s number one.
Ter Stegen, 23, has only played a handful of league matches for Barcelona since arriving from Borussia Mönchengladbach in the summer of 2014, with Luis Enrique preferring to use the Germany international in the Champions League and Claudio Bravo in La Liga.
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Ter Stegen is widely regarded as one of the most promising young goalkeepers in world football and has enhanced his burgeoning reputation over the past calendar year by playing in the Copa del Rey and Champions League finals - both of which Barcelona won - as well as the UEFA Super Cup.
Having two keepers - one for the league and another for cup competitions - clearly worked for Enrique and Barcelona last season, but Ter Stegen appears to be frustrated with his lack of action in La Liga and understandably so.
Ter Stegen has a huge release clause
The chance of playing week-in, week-out for Liverpool would naturally appeal to the former Gladbach star - although in order to secure his services the Reds may need to trigger his astronomical €80 million (£56 million) release clause.
There’s virtually no chance that Liverpool would be prepared to pay close to that fee, but there might be an opportunity to land his signature for a lower price if he tells Barcelona he wants to leave.
Barcelona can't afford to risk losing Ter Stegen
With Bravo set to turn 33 in April, however, Barcelona are unlikely to allow Ter Stegen to quit the Camp Nou without a fight.
Such transfer stories may also be designed to encourage Enrique to start using Ter Stegen more at Bravo’s expense.
Liverpool fans: should Jurgen Klopp replace Simon Mignolet with Marc-Andre ter Stegen? Have your say by leaving a comment in the box below!