Besiktas have given up their right to sign Anderson Talisca on a €21 million move.
The Black Eagles had a buyout option for the Brazilian attacker that expired on 31 May.
The Istanbul giants have decided not to take up the cut-price deal with Benfica.
The Eagles €40m valuation is almost double what the Istanbul giants would have had to play.
Portuguese publication the Record report that Liverpool are now favorites in the race for Talisca.
Per the source, Benfica do not want to keep Talisca on but he is under contract at the club until 2021.
The Brazilian has made it clear he wants a Premier League move but has not opened up about which club he could end up joining.
Manchester United, Wolves and Juventus have also been linked with the 1.91m tall attacking midfielder recently.
Talisca spent two seasons on loan at Besiktas, winning the league title and helping the Istanbul giants cruise through the 2018-19 Champions League group stage as undefeated leaders.
The powerful attacker scored 20 times and provided eight assists in all competitions this season, in total Talisca netted 36 goals in 79 games for Besiktas.