Vermaelen is recovering from an Achilles problem while Sebastien Squillaci is out with a hamstring injury sustained in the 1-1 draw against Leeds United in the FA Cup on Saturday.
The French central defender will only be out for two-to-three weeks but Wenger could not say when Vermaelen would be fit again and therefore may have to bring in a replacement.
"He (Vermaelen) had another setback on Saturday that we are concerned with," Wenger was quoted as saying on the club's website.
"We are consulting top specialists around the world. We'll know more on Wednesday.
"Unfortunately, I can't give you any precise date but I concede that, with this little setback from Thomas, we are in a situation where we will have to look around.
"Squillaci will be out for a maximum of three weeks, minimum two. It is a hamstring injury but it is not too bad - a grade one. He'll be back in two weeks if all goes well."
Wenger said that while he had "internal solutions" he also knew the sort of player he was looking for.
"Ideally it would be better if they were adapted to English football," he said. "If you need players now in January then you cannot wait three months before they can play.
"If the opportunity turns up we will fetch it but, if not, I believe we can cope.
Arsenal visit Ipswich Town in the first leg of their League Cup semi-final on Wednesday before travelling across London to play Premier League basement club West Ham United on Saturday.
Wenger's side are third in the standings four points behind leaders Manchester United who also have a game in hand.
