Arsene Wenger sent his scouts to run the rule over the Dutch centre half in Celtic’s Europa League clash with Dinamo Zagreb, and received a glowing report.
The former Groningen defender had been linked with Sunderland and Southampton during the summer, with the Hoops knocking back all offers for the 23-year-old.
Van Dijk was left out of the squad that drew 1-1 with Dundee after Ronny Deila felt deadline day speculation may have unsettled the Dutchman.
However, van Dijk has insisted that he was not looking for a move away from Celtic in the summer, and remains committed to the Parkhead club - but hinted that he would have moved if it had been to a Champions League club.
Celtic have already suggested they are in no hurry to sell their prize assets, after Fraser Forster joined Southampton for £10 million.
But Arsenal could test Celtic’s resolve with a large bid in January.