Van Dijk signed a five-year deal last year and Liverpool have so far refused to comment. "We do not need to sell any player for the first time since I've been here".
Celtic, who sold the centre-back for £13million in September 2015, stand to pick up 15 per cent of the south coast club's transfer profit if - or when - Van Dijk moves on.
Liverpool, though, are yet to confirm a fee with Southampton.
Jurgen Klopp made the Holland global a transfer priority having guided Liverpool into the Champions League play-offs but faced competition from the Premier League champions, Chelsea, and Manchester City for the 25-year old.
Football journalist Andy Brassell then correctly stated that the fee is nearly irrelevant, because Liverpool can afford it and there aren't many great central defenders available.
"He's proven himself at Celtic, he's gone to Southampton who are, I'm not trying to be disrespectful but they're an average Premier League team".
What makes the 25-year-old so widely chased by clubs is his combination of physical strength, pace, and his skillful play-making from the back. Two of those players are on the wane - Yaya Touré and Zlatan Ibrahimovic - but the other should be approaching his prime.
Saints have endured miserable summers for the past three years, losing several of their biggest stars as well as seeing bosses Mauricio Pochettino and Ronald Koeman quit.