Van Dijk has been heavily linked with a move away from Southampton this summer, with the Saints said to be looking for at least £70million to sell.
Liverpool and Manchester City have both registered interest in the defender - and now The Sun claim Arsenal could make a move.
The Gunners have already broken their transfer record this summer to sign striker Alexandre Lacazette as they look to end their 13-year wait for a Premier League title.
Arsene Wenger switched to a three-at-the-back formation towards the end of last season and could look to bolster his options in defence.
However, The Sun suggest Arsenal will struggle to land Van Dijk without Champions League football, having only qualified for the Europa League.
Liverpool looked set to sign the 26-year-old defender before they were forced to publicly end their pursuit.
Southampton reported Liverpool for making an illegal approach for Van Dijk - but reports suggests the Reds could still sign the Dutchman.
Van Dijk joined Southampton in 2015 from Celtic for £13m and is contracted at St Mary's until 2022 after penning a new six-year deal last year.
Southampton executive director Les Reed recently revealed that none of the club's top players are for sale this summer, including Van Dijk.
"None of those players are for sale," he told Sky Sports when asked about Van Dijk and right-back Cedric Soares.
"I can't make it any plainer than that and that's the way we mean to go forward.
"We built this squad over some time and think we have a strong squad. We will fine-tune it but, other than that, we are looking forward to a very competitive season and we plan to go forward on that basis.
"There may be players that go on the basis that it is the right thing for them and the club at that given time.
"But we don't expect that to be wholesale and this is simply doing sound business in the transfer window."
Source: Daily Express