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The Spaniard, who signed from West Ham United in the summer of 2019 on a free transfer, is mulling over the terms as he weighs up his next move.
The contract offer comes just days after Hans Leitert was announced as Fenway Sports Group's new global head of goalkeeping with the Austrian tasked with installing a new coaching department at Anfield.
Elsewhere, the Reds have also confirmed that Mateusz Musialowski, Melkamu Frauendorf and Adam Lewis will all leave the club this month.
Left-back Lewis has spent the last two seasons on loan with Newport County and was part of an academy side who played in the FA Cup win over Shrewsbury Town in the FA Cup at Anfield in 2020.
Liverpool also formally confirmed the exits of Thiago Alcantara and Joel Matip, whose final seasons at Anfield were both wrecked by injury problems.
Academy players Nathan Giblin, Francis Gyimah, Luke Hewitson, Niall Osborne and Cody Pennington are also leaving the club, bringing the total up to 10.
Liverpool's official released list: Thiago, Matip, Lewis, Frauendorf, Musialowski, Gilbin, Gyimah, Hewitson, Osborne, Pennington.
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