Captain Virgil van Dijk says there has been "progress" in negotiations with Liverpool over a new contract.
The 33-year-old is out of contract at the end of the season and the centre-back said in March he had "no idea" if he would remain at Anfield.
The defender is one of three high-profile Liverpool players to be nearing the end of their deals, with Mohamed Salah and Trent Alexander-Arnold also yet to sign extensions.
But, speaking to reporters following the 3-2 defeat by Fulham on Sunday, Van Dijk was more positive about the prospect of staying at the club.