The 23-year-old has been the subject of transfer speculation in recent months, with the Gunners reported to be preparing a January bid.
Van Dijk has admitted that he is not ruling out leaving Parkhead in the future, telling the Daily Star: "Arsenal are an amazing club. It's a big club with a great history.
"I'm happy here [at Celtic] just now and I want to play well and we'll see what happens in the future. Until there are bids I can't say a thing. There is no rush to leave but you never know in the future."
The Dutchman joined the Hoops from Eredivisie outfit Groningen last summer for £2.6m.