The Bluebirds boss, though, has stopped short of completely shutting the door on future interest.
Reports in France have suggested Barry-Murphy is among the candidates Strasbourg are considering should their current head coach, Liam Rosenior, depart for Chelsea.
Rosenior is believed to be poised to replace Enzo Maresca following the Italian’s recent exit from Stamford Bridge, with Strasbourg part of the BlueCo ownership group that also controls Chelsea.
When asked about the rumours, Barry-Murphy was quick to stress his contentment in the Welsh capital.
“I don't know. I love Cardiff,” he said.
“I love being at Cardiff, I love it. I feel very lucky to be here.”
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The former Manchester City Under-21s coach has made an outstanding impression during his first six months in charge, guiding the Bluebirds to the summit of Sky Bet League One while implementing a vibrant, attack-minded style of football.
Cardiff reinforced their promotion credentials on Sunday with a 1-0 home victory over Wigan Athletic, maintaining a three-point cushion at the top of the table.
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Captain Calum Chambers’ superb strike proved decisive, although Cardiff could have wrapped up a more emphatic win but for a series of saves from Wigan goalkeeper Sam Tickle.
Barry-Murphy admitted he would have welcomed greater ruthlessness in front of goal.
“Would have liked to score more goals to make it more comfortable near the end and get the supporters more of what they wanted,” he said.
Despite that, the Irishman reflected positively on a demanding festive schedule that saw Cardiff take 10 points from a possible 12.
“But the efforts of the players in the past two weeks to win three and draw one of our four games in this 10-day period, it was something that I’m very grateful for,” he added.
The head coach also underlined the importance of Cardiff City Stadium as a platform for success, pointing to their strong home form as a cornerstone of their promotion push.
“It’s been brilliant for us playing at home in the season, so we want to continue that and every time we come here, we’re looking to keep playing the way we want to play and score goals and keep clean sheets,” he said.
“To continue that run is very important for us to be where we want to be.”
While transfer speculation intensifies with the January transfer window open, Barry-Murphy appears unfazed, insisting his attention is firmly on improving his current squad rather than entertaining outside interest.
“I didn't really know about it [the speculation], that's for sure,” he said.
“We just focus on ourselves and try to keep improving all the time.”
He also reiterated his belief that Cardiff have enough firepower throughout the team to sustain their title challenge.
“The biggest thing for us is to understand how we’re creating chances, keep doing it, do more of it, then we have goals throughout our team,” Barry-Murphy said.
“We’re very confident over the course of the season that we’re scoring enough goals to be successful.
Wigan manager Ryan Lowe, meanwhile, cut a frustrated figure after watching his side manage just three shots on goal and limited penalty-box presence as they slipped to 15th in the table.
“Disappointed, I thought the lads were solid and resolute in the last part of the game and we knew we had to come here with a different gameplan and stay in the game for as long as we can,” Lowe said.
“We did that, yes they had large parts of the ball, we could have done a little bit better with the ball, we’re turning the ball over a little bit too easy.
“They do the ground work, they’re getting across the pitch with the distances they cover, but I’m asking for a little bit more with the ball and we didn’t really have that.”
