The Sun says Wenger will launch a £9million bid for Cole if Nicklas Bendtner fails a Friday fitness test.
The Arsenal boss admitted: "There is no way we can carry on with only one striker.
"Bendtner is being treated now and will come back on Friday for tests. If he is out For another two months, we will need to buy someone, absolutely."
Dane Bendtner returns to the club for a series of medical tests this week after missing Arsenal's last 14 games with a groin injury.
And with Robin Van Persie unlikely to play again this season, Wenger needs more firepower.
Wenger said: "There is a 50-50 chance we'll sign somebody. Even if Bendtner is OK we will look around and if we find a good bargain we will still do it."
Unlike other potential targets, Cole would be eligible to play in this season's Champions League.
And crisis club West Ham would not stand in the way of his departure for the right price.