After losing their opening Premier League match 3-1 at home to Aston Villa, the north Londoners have been revitalised by the signing of Germany playmaker Mesut Ozil and are unbeaten in the 11 matches they have played in all competitions since.
The Premier League leaders are without a trophy since 2005 but ex-Arsenal striker Bergkamp believes they can end that barren run by winning the title in May.
"He (Wenger) has silenced the critics a little bit although you never know what will happen in the season," the former Netherlands international told talkSPORT radio.
"For now they're doing really well. They bought a terrific player in Mesut Ozil. It's going well at the minute.
"It's still early days of course but they're now going into November, a month where Arsenal are known for having problems. If they are still up at the top of the league in January or February I think they've got a good (title) chance."
Bergkamp joined Arsenal from Inter Milan in 1995, playing 423 times for the club in 11 years and scoring 120 goals.
He won the league on three occasions and the FA Cup four times and was a key part of the club's undefeated league season in 2003-04.
Having been a part of Wenger's golden era, Bergkamp says the criticism the Frenchman received in the close season was unjustified.
"I was really surprised by the stick Wenger got this summer," he added.
"Looking back over the last six or seven years where there weren't any trophies it was disappointing. But can you blame just him I don't think so," said Bergkamp who is now on the coaching staff at Ajax Amsterdam.
"He's a manager who wants to win trophies. He wants to be successful. He's not doing it on purpose."
Arsenal, who lead Liverpool on goals scored at the top of the table, host Norwich City on Saturday.
Bergkamp said he would like to work for the north London club again in the future.
"I would love to go to England some time, preferably Arsenal," he said in a separate interview with Sky Sports television.
"But I don't see myself as a head coach or manager. I see myself as part of a coaching team."