The Premier League champions are said to be ready to offer £50million for van Dijk's signature but Southampton remain determined to hang on to the former Celtic man.
He said he felt "frustrated" and "disappointed" that "enquiries from multiple top clubs have been consistently rebuffed".
"It is with regret that I can confirm that I have handed in a transfer request to leave Southampton Football Club", van Dijk's lengthy statement read.
Van Dijk, capped 12 times by the Netherlands, said the saga had "seriously affected" his relationships with people at the club and Southampton's fans.
"Just at the moment I'm fine".
Liverpool were forced to issue a statement apologising to Southampton over their pursuit of Netherlands worldwide Virgil van Dijk. Disappointingly, these conversations have regularly found their way into the media.
"I have never once refused to train, I was open and honest about my frame of mind and I did not feel I was in a settled mindset".
"He's a strong competitor as a central midfielder and will complement our existing midfield players, and he is also a really good age at 25; we are absolutely delighted to welcome him to the club".
Van Dijk is depserate to leave the Saints and had chosen to move to Anfield before Liverpool retracted their interest.
It remains to be seen how this situation will develop and play out but it is hard to see how the Dutch defender can be part of the Saints side when they begin their Premier League campaign against Swansea City next weekend at this stage.
'We need more players, not top level like Neymar but more players to improve our squad and our quality'.
He has two-and-a-half weeks to find a new club.