Casillas, who recently made his 1000th career appearance, is out of contract at the end of the season and will be available to clubs as a free agent.
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According to TMW, the Reds are targeting the Porto stopper as a replacement for Simon Mignolet, who has been replaced as the club’s first-choice goalkeeper by Loris Karius.
The source adds that the Spaniard, who is keen to continue playing in Europe, may be tempted by a switch to the Premier League.
Casillas lined up against Jurgen Klopp’s side in the Champions League last-16 second leg at Anfield earlier this season, after which the 36-year-old received applause from Liverpool faithful.