According to the Mirror, the Dutch defender's signing has become Antonio Conte's number one priority. The latter's side are leading the Premier League table with 69 points after 28 games, 10 points ahead of the second place Tottenham Hotspur.
The west London club are the favourites to win the league and are assured to qualify for the next season's Champions League. The Italian boss is looking to bolster his defence as the Stamford Bridge outfit prepare to return to the European stage.
Van Dijk, who moved to St Mary's Stadium from Celtic in 2015 has been in fine form for the south coast club. Under the guidance of Claude Puel, the Dutch international has been the star player for his side until he picked up an ankle injury in his side's league win over Leicester City in January.
The influential and much sought after central defender has a lot of suitors as his form has attracted interest from the top clubs in the Premier League. The Mirror claims Chelsea's league rivals Manchester City and Jurgen Klopp's Liverpool are interested in signing the defender. Pep Guardiola is an admirer of the defender and has identified Van Dijk as the player to strengthen his side's defence.
In addition to this, Van Dijk's former manager Ronald Koeman is looking at the option of bringing him to Everton. Manchester United are also in the race for Southampton captain's signature, reports The Sun.
However, Chelsea remain confident of beating other Premier League clubs in securing the services of the 25-year-old in the upcoming transfer window. Van Dijk is valued at £50m ($62.4m) and the league leaders willing to meet Southampton's asking price.
Southampton have publicly insisted that Van Dijk is not for sale. However, the Saints will face an uphill battle in retaining their star player beyond the summer. John Terry, 36, is likely to leave Chelsea after his contract expires at the end of the season and the Dutchman could take his place in the Blues squad, if he decides to swap St Mary's Stadium for Stamford Bridge.