The Netherlands international defender has been quoted as saying by BBC Sport that he would like Southampton to consider interest in him from top clubs.
The 26-year-old former Celtic and Groningen star has also been quoted as saying that he is “incredibly ambitious”.
According to The London Evening Standard, Antonio Conte's Chelsea and Jurgen Klopp's Liverpool are interested in signing Van Dijk from Southampton in the summer transfer window.
It has also been reported that the 26-year-old Dutch centre-back is rated at £50 million.
Southampton legend Le Tissier, who now works as a pundit for Sky Sports, has taken to Twitter to give his reaction to Van Dijk handing in a transfer request at Southampton.
Meanwhile, former West Ham United and Queens Park Rangers defender Danny Gabbidon has urged Liverpool manager Klopp to make a move for Van Dijk now.
read VVD statement. Who suggested he refused to train? And I thought he was only interested in signing for Lfc but mentions top club(s) now— Matt Le Tissier (@mattletiss7) 7 August 2017
As an ex pro I'm embarrassed whenever I hear of a player refusing to play and still want his wages whatever club that's at https://t.co/Z9XH9eRMAi— Matt Le Tissier (@mattletiss7) 7 August 2017
He's not going to say 'liverpool' specifically is he!? As an ex-pro I would have thought you'd see that. Bitter Southampton fan? Hmmmm— Thomas Yeowart (@thomasyeowart) 7 August 2017
Why sign a 6 yr contract here if he was that ambitious?? https://t.co/E1UxR0VaUv— Matt Le Tissier (@mattletiss7) 7 August 2017
Maybe he has a bit of ambition unlike yourself !!— matty houltby (@pistolmatty) 7 August 2017
A lot of people forgetting that Liverpool publicly stated they ended their interest in VVD surely if they now bid they'll look a bit foolish— Matt Le Tissier (@mattletiss7) 7 August 2017