Karius joined Besiktas on a two-year loan deal in 2018.
The German goalkeeper, however, has failed to impress at Besiktas with the Turkish club set to reject the option to make the deal permanent this summer.
Instead, they have Nyland on their short-list as a potential replacement.
Nyland join Villa from FC Ingolstadt on a three-year deal back in 2018. The Norwegian was signed as a back-up, but he ended up playing 23 Championship games last season as the Villans secured promotion.
The arrival of Tom Heaton and most recently Pepe Reina have pushed Nyland down the pecking order at Villa Park. He has made just one Premier League start in the 6-1 defeat at home to Manchester City.
Nyland, however, may get the chance to feature in the Carabao Cup final.
His contract at Villa ends in 2021. The Midland club may feel it is in their best interests to sell him then when Heaton makes his expected recovery from injury.
Besiktas reportedly have the 29-year-old on their short-list as the Turkish club have no obligation to sign Karius this coming summer.
Karius, who joined Liverpool for £4.7 million in 2016 (Telegraph), has made 20 league starts this season.
The 26-year-old is most remembered for his two errors in the 2018 Champions League final after making over 30 starts for the Reds in the 2017-18 campaign.
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