Vermaelen has not played for the Gunners since August 28 after the Belgium star suffered an Achilles injury while on international duty.
It had been hoped the 25-year-old would only be sidelined for a couple of weeks, but complications have now resulted in Arsenal being unable to put any timeframe on his return.
With French centre-back Sebastien Squillaci out for a month after suffering a hamstring strain during Saturday's 1-1 draw in the FA Cup clash with Leeds, Wenger admits he is likely to be forced into the transfer market during the January transfer window.
Wenger, who only has Laurent Koscielny and Johan Djourou available to play centre-back, has been linked with Bolton's Gary Cahill, Montpellier's Bosnian international Emir Spahic and Werder Bremen's Per Mertesacker.
"Vermaelen had another setback on Saturday that we are concerned with," Wenger told Arsenal TV Online.
"We are consulting top specialists around the world. He has another check today, and we will 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 will be back in two weeks if all goes well."