The Dutchman is one of three key Liverpool players out of contract at the end of the season, along with Mohamed Salah and Trent Alexander-Arnold.
As it stands, Van Dijk will be able to start discussions over a pre-contract agreement with overseas clubs from January 1.
However, the experienced centre-back has indicated he would rather extend his stay with Liverpool than seek a fresh challenge at the end of the season.
Liverpool table Van Dijk contract offer
According to The Athletic, Liverpool have already made an opening contract offer to Van Dijk as they look to step up their efforts to retain the defender's services.
However, the report claims that the Netherlands international rejected the proposal after it 'fell short of his expectations'.
Talks are believed to be ongoing but there has been no breakthrough about the crucial details of the new deal, including the salary and length of the contract.
The Merseyside club will be determined to find a way to break the stalemate, with Van Dijk still regarded as a key part of the Liverpool side.
The Reds skipper has played every single minute of Liverpool's Premier League campaign, helping the club win 11 of their 14 league matches (D2, L1) to leave them seven points clear at the top of the table.
Liverpool expected to table Salah offer in near future
Salah has been left exasperated by the lack of progress in contract negotiations after he previously revealed that he was yet to receive an offer.
However, the same report from The Athletic states that the situation will 'change soon', with Liverpool expected to step up their efforts to keep their star forward.
The Egypt international continues to showcase his importance on the pitch, having scored 15 goals and provided 12 assists in 21 competitive appearances this season.
Salah scored a brace and registered an assist in Wednesday's dramatic 3-3 draw against Newcastle United at St James' Park.
The 32-year-old will look to continue his fine form when Liverpool take on local rivals Everton in Saturday's Merseyside derby.
Written by
Ben Sully