Wenger: Arsenal seeking January signings
Wenger had said earlier that he was unlikely to spend and was happy with the squad but losing the Dutch striker for four to five months with an ankle injury has changed his thinking.
"I didn't feel we were in the need to buy anybody but we will be out on the market that is for sure now," he told the Arsenal website.
"However we will only make a decision if it suits us."
Arsenal are fourth overall and 11 points behind Chelsea in the Premier League, although with a game in hand, after losing to the leaders 3-0 at the Emirates Stadium at the weekend.
The Dutchman, who had scored eight goals in his last 11 matches for Arsenal, was injured in a friendly between Netherlands and Italy last month after landing badly following a tackle.
The North London club have also lost England under-21 fullback Kieran Gibbs for three months after he broke a bone in his left foot last month, while Danish forward Nicklas Bendtner is recovering from groin surgery.