Bendtner had been seen as a solid back-up to lead frontman Olivier Giroud and came off the bench to score a late goal which helped beat Cardiff City on New Year's Day, only to sprain his ankle in the process as the Gunners moved back to the top of the English Premier League.
Arsenal are examining the full findings of a scan, and following further consultation with specialists, Wenger is likely to have a clearer idea of the diagnosis by the time he faces the media again after Saturday's FA Cup third-round tie against Tottenham Hotspur at the Emirates Stadium.
Giroud missed the 2-0 win over Cardiff because of his own minor ankle problem and has now also been hit by a sickness bug, so is not expected to play in the north London derby. Summer signing Yaya Sanogo, meanwhile, is only just recovering from a back injury.
Arsenal do have Germany forward Lukas Podolski fit again, but he looked rusty when deployed in a central role against the Bluebirds.
Given Arsenal's lack of extensive cover, Wenger understands should Denmark forward Bendtner - who had looked on the verge of leaving the club in the summer window - be set for a prolonged spell of rehabilitation, then the club will have no choice but to bring in reinforcements
"If it is a question of up to three weeks, okay, but if it is a question of months (then) the situation is quite (different), so that is what we have to determine," said Wenger, who played down reports Arsenal were closing in on a £2m move for Dimitar Berbatov.
"We don't rule anything out," Wenger said. "If Bendtner is out for a long time, that is the obvious position. We (would) have to (buy)."
Winter transfer blues
Wenger accepts whatever option he eventually decides, January is not the best time to try to land the ideal target.
"Honestly, you want to keep your chances in the season at the best possible level. Is it for short term or a stop-gap? Ideally, you want a longer solution, but a longer solution looks much more difficult to find in January than a short gap," the Arsenal manager said.
"You can find a solution somewhere - a club that has financial trouble and wants to get rid of a big contract for five or six months, but to find in January exactly the player who will be tomorrow's star on the longer term is much more difficult."
Arsenal were dumped out in the fifth round at home by Blackburn Rovers in February 2013, which effectively ended hope of a trophy.
Wenger, though, maintained: "This season is different because we are fighting in the Premier League. Last year when we played Blackburn it was one of the remaining targets of the season, but this year because we are in a strong position.
"It will not stop us from focusing on the Premier League, but still it is better to go through."
Spurs have found some form under new boss Tim Sherwood to record a hard-earned 2-1 win at Manchester United on New Year's Day. Wenger has seen off ten managers at White Hart Lane since he took charge of Arsenal.
He said: "Stability is important if you want to create a style of play, an educational style in your club and if you want financial stability. Tottenham have always had good teams and good players since I have been here, but we have always just been a bit more than them."
Wenger added: "Sherwood knows the young players well and will know well who can make it at the top level or not. They have signed him only for 15 months, so let's see (what happens)."