“I am incredibly ambitious and want to achieve as much as I possibly can to fulfil my potential in what is a very short career as a professional footballer,” Van Dijk said in a statement released to the media.
“I want to play European football again and challenge for major honours and as such I would like Southampton to consider the interest in me from top clubs should it still exist.”
Van Dijk, 26, has been linked with Liverpool, Chelsea and Manchester City.
Liverpool publicly dropped their interest in signing him earlier in the close season after Southampton threatened to report them to the Premier League for an illegal approach.
Van Dijk revealed he had been fined two weeks’ wages by Southampton and said he would be appealing against the punishment, which he described as “unjustified”.
He said he felt “frustrated” and “disappointed” that “enquiries from multiple top clubs have been consistently rebuffed”.
He also rejected accusations he had refused to train and said he had been told by new manager Mauricio Pellegrino to train away from the first team due to his unsettled mindset.
“As a proud professional I am insulted by the suggestion that it was me who refused to train and so feel it is important to point out the true version of events,” he said.
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.
“I would like to make clear that I have nothing but gratitude to everyone at Southampton for giving me the opportunity to play in the Premier League,” he added.
“However, the time for me to move on is now and I hope to be able to work with the club to find the best resolution to suit all parties.”
Van Dijk joined Southampton from Celtic in a £13 million ($16.9 million, 14.4 million euros) move in September 2015 and has since emerged as one of the most imposing centre-backs in the Premier League.
He signed a new six-year contract in May 2016.
He missed the last five months of last season, including Southampton’s 3-2 loss to Manchester United in the EFL Cup final, due to an ankle injury.
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