The Dutchman has been linked with a move away from the south coast club all summer and handed in a transfer request on Monday.
In his statement, a fiery van Dijk hit out at the club and rebuffed any suggestion that he had refused to train.
It now looks certain that the defender will leave with Liverpool, Chelsea and Manchester City all likely destinations for the 26-year-old.
However, Wright believes Arsenal should be throwing their hat into the ring.
“We haven’t signed the players that people are constantly talking about, who are going to lead Arsenal,” said Wright on BBC Radio 5 Live.
“At some stage during the season they’re going to need those players and that is where the test is going to come.
“Now it’s Leicester, Stoke and Liverpool just to start and the pre-season hasn’t gone fantastically.
“I would have definitely tried to get van Dijk. I would be going in very strong.”
Wright also believes Arsene Wenger should have tried to sign Nemanja Matic.
“To see that Matic has left Chelsea and gone to Manchester, can you persuade him to stay in London? He’s in London, he’s settled, can you get him to come to Arsenal because that is what Arsenal need. That player. That type of player.”