The 26-year-old's impressive form in the first half of last season has seen him being linked with a host of clubs in England. Liverpool were believed to have won the race for Van Dijk's services in June.
However, the Merseyside club were forced to end their interest in Van Dijk after they issued a public apology for "any misunderstanding", while there were suggestions the Saints were planning to report Liverpool to the Premier League for the alleged illegal approach.
According to the Daily Mail, Southampton have so far refused to sanction the Dutch international's sale this summer, even though the central defender is keen on leaving his current employers.
Southampton manager Mauricio Pellegrino has already said that the Dutchman is not involved with the team psychologically. Van Dijk has been omitted from the Saints' squad for their pre-season trip to France.
Liverpool are still believed to be interested in securing the centre-back's signature. Jurgen Klopp's side are not the only club keen on signing the Southampton star. The Reds' league rivals Manchester City and Premier League winners Chelsea are also in the race for Van Dijk.
Van Dijk's camp remains hopeful that Southampton will allow their player to leave the club before the end of the transfer window. Liverpool, Chelsea and City are now preparing to make bids for the former Celtic star.
Southampton are looking at a contingency plan if the defender does leave the club. They have identified Wimmer as a player who can replace Van Dijk at the south coast club. The 24-year-old moved to White Hart Lane from FC Koln in 2015 and has struggled to cement his place.
The Austrian international made only four starts in the Premier League last season. Mauricio Pochettino is not willing to allow Wimmer leave, but is aware that the player is looking for a move as he seeks regular playing time. Southampton believe an offer of around £20m ($26.3m) should be sufficient for them to prise Wimmer away from White Hart Lane.