Captain Virgil van Dijk says he had “progress” in talks with Liverpool on a new deal.
The 33-year-old excluded his contract at the end of the season and the midfielder said in March he had “had no idea if he stayed at Anfield.
The defender is one of Liverpool’s three top players, who are close to the end of their contracts, and Mohamed Salah and Trent Alexander Arnold have yet to sign extensions.
However, in an interview with reporters after the 3-2 defeat to Fulham on Sunday, Van Dijk was more positive about the horizon of staying at the club.
“There is progress, yes,” the Dutch captain said.
“I don’t know (if I stayed), we see. Listen, these are internal discussions and we see.
“I love the club, I love the fans and they were there for us and we wanted to reward them,” he said.
“But I want to be there again on Sunday (at home for West Ham United) and make the stadium an amazing place for us as usual.
Liverpool are 11 points clear at the top of the Premier League despite their defeat in western London.
Craven Cottge’s defeat was Liverpool’s second defeat this season and his first defeat in 26 appearances.
“It was a poor day in the office for all of us,” Van Dick added.
“There was an individual time that they should have been treated better. It was not accepted as a team.
Van Dijk joined Southampton in 2018 on a £75m deal.
He has scored 26 goals in 323 appearances for the Reds and has been the main defender, as Jürgen Klopp has won twice in the Premier League, the Champions League, the FA Cup, the UEFA Cup and the FA Cup.