Liverpool now expect Simon Mignolet to stay at the club beyond this summer.
Mignolet was tipped to end his six-year association with the Reds in pursuit of regular first-team football elsewhere after losing his place to Alisson Becker.
Anfield chiefs had set a £15 million price tag for the goalkeeper amid interest from several Premier League clubs including newly-promoted Norwich City.
But the Times claim that Mignolet will instead remain on Merseyside unless a permanent offer matching both the player and the club’s expectations is tabled.
The 31-year-old last summer questioned Liverpool’s ‘bizarre’ decision to allow Loris Karius to join Besiktas on loan after denying him a similar move.
Napoli and Fulham both expressed an interest in signing Mignolet, who has two years remaining on his current Anfield contract, but failed to secure a deal.
However the Belgium international has since impressed Jurgen Klopp with his handling of the demotion to both Alisson and Karius in successive seasons.
It means Liverpool are unlikely to be in the market for a new back-up goalkeeper despite identifying several Premier League stoppers during recent months.
Southampton’s Alex McCarthy had emerged as Mignolet’s most likely successor, having himself fallen out of favour on the South Coast over the past 12 months.