Gibbs has shaken off recent injury setbacks and is now a solid member of the Gunners defence.
Following the international retirement of Cole after not being selected for the World Cup by Roy Hodgson, Everton's Leighton Baines and, if fully fit, Manchester United teenager Luke Shaw look set to be the preferred options for the European Championship campaign, which continues next week against San Marino and then Estonia.
Gibbs, however, is the only English left-back with Champions League action this season, as Arsenal prepare for Wednesday's Group D tie against Galatasaray at the Emirates Stadium.
Wenger believes Gibbs - with only three senior England appearances, the last coming after a three-year absence against Germany in November 2013 - can go on to emulate Cole, who was first choice for both Arsenal and then Chelsea while earning a century of international caps.
"Kieran looks to me that he's going into second gear now and he realises that he can trust his body, he can trust his talent," said Wenger of the Arsenal Academy graduate.
"He has such a great potential that now if he just lets it go, because he can dribble as well, because when he arrived at the club he was 16 and he was a winger, midfielder, and I saw that potential didn't really come out.
"I saw he was intelligent and maybe I could transform him into a defender
It was a bit similar to Ashley Cole.
"We try always to show him confidence.
"I let Gael Clichy go because he was a young, English left-back
That's the main reason I left Clichy go
I wanted to give him a chance.
"Against Tottenham on Saturday he showed his personality to impose himself on the game and took the game by the scruff of the neck for a long period in the second half and that's what you want to see from him because all the talent is there.
"For a long time it was Ashley Cole (for England), (there was) no discussion
Now it is a bit more open."
Wenger continued: "It is a good example (for Gibbs) to follow because Ashley is top.
"You see stories about Ashley Cole, but on the day of a game, when it mattered and when you had to be there, he was always there
You have to respect that."
Arsenal will be without Wales midfielder Aaron Ramsey for at least a month because of a hamstring injury picked up against Spurs, while captain Mikel Arteta is also sidelined by a calf problem.
England's Jack Wilshere, however, has recovered from a twisted ankle.
Wenger maintains the club, having brought in a new fitness coach Shad Forsythe, who worked previously with the German national team, continue to take advice on possible causes for any soft tissue injuries, even to analysing the Emirates Stadium playing surface.
"We are getting things together, getting a report on all the different opinions, what happened to him (Ramsey)
It is a real concern" said Wenger.
"We made a lot of changes, in the way we prepare, in the way we work on prevention for injuries.
"We have not found out why it happened.
"When you work on the prevention for injuries it's a question mark 'why do you get the injuries?'
"We know a lot more than 18 years ago than when I arrived, but still not enough to predict 100 per cent scientifically what happens to everybody."
Meanwhile, on Wednesday, Wenger will have been at Arsenal for 18 years.
The French coach, who turns 65 in October and last season marked 1,000 matches in charge, insists he "never looks back", but continues to believes in the "huge potential" of his current squad
The Gunners boss has never won the Champions League, reaching the 2006 final where they were beaten 2-1 by Barcelona in Paris.
"It is much more predictable today, the outcome of the Champions League, than it was 10 years ago
It is harder to win it, but as well more exciting," Wenger said.
"If you make a poll tomorrow and say to people 'give me four clubs who will win the Champions League', then 80 or 90 per cent of people will say 'there are these four clubs'.
"I don't think that we are one of the four who will be favourites to win it, but football is strange - and not always predictable, so let's first qualify from the group stage and then we will see."
Source : PA