The centre-back, who won his fourth cap against the Azzurri, was one of the stars of Wales's 2-1 win on Wednesday and his polished performance again raised the question whether City can hold on to their 23-year-old jewel when the Premiership transfer window reopens in January for a month.
Chelsea and Everton have been among the clubs trailing the former West Bromwich Albion defender but Gabbidon says he has no desire to leave the Bluebirds. "I'm happy playing for Cardiff," he said. "Things are going well here and I've no intention of leaving the club. There might be interest in me. When a player does well at international level that is bound to happen.
"But I'm very happy at Cardiff. We've got a very good side here and I feel we're on the verge of doing something. I don't see any reason why I should want a change.
"I think we can win promotion this season and, who knows, then reach the Premiership."
Speaking 15 hours after the epic tussle with Italy, Gabbidon, who was stagnating in West Brom's reserve side before joining City in the summer of 2000, said victory had "still not sunk in".
"Before the game I was in our hotel thinking I would be playing against players that I was watching on TV only a couple of years ago," said Gabbidon, whose next assignment comes for City at Blackpool tomorrow.
"That was the nearest I got to dreaming. But once I was on the pitch I saw them as normal players.
"You can't start thinking, `He's a great player. I'm in awe of him.' To walk out onto the pitch alongside players like Ryan Giggs and Del Piero still hasn't sunk in because I'm still a Division Two player."
From marking Juventus superstar Del Piero in front of a 72,500 crowd, Gabbidon will track John Murphy in front of around 8,000 at Bloomfield Road.
"It will be strange to go from playing against a world-class side like Italy to playing in a Second Division game against Blackpool," said Gabbidon. "But I'll be treating this game the same as I treated the Italy match. It's tiring playing in a game such as the one against Italy but I've got a few days to recover.
"As far as I'm concerned, the Blackpool game is another big match because I want to win promotion with Cardiff.
"If you said to me a couple of years ago that I would be playing for Wales and challenging for promotion with Cardiff I would have laughed in your face. It's amazing how so much has happened to me in such a short space of time."