The Red Bull Salzburg head coach admitted it is an "honour" to be linked with the Parkhead club after a number of ex-players including club legends John Collins and Pat Bonner identified the 47-year-old American as a potential candidate to replace Neil Lennon.
Marsch is on the verge of guiding Salzburg to second consecutive Austrian league and cup double, having previously coached New York Red Bulls, winning the MLS coach of the year in 2015.
He also had a spell as assistant manager at Red Blul Leipzig, and has described himself, perhaps appropriately, as an “energy drink” for his forceful man-management and high-pressing on-pitch approach.
He described the Celtic role as “interesting” and admitted he was intrigued by the prospect of a move to Glasgow.
"I've heard [about the links]. It's an honour for me," Marsch told BBC Sport.
"Three or four years ago, being linked with a club like Celtic would literally be an impossibility for me. And now that this is where I am, I always just try to look at it in terms of, 'what would the project look like?'
"Would we have similar ideas in how to build it the right way, invest in the academy, invest in young players and create this development process that I'm talking about? And not just focus on winning.
"Obviously I know that when you're the coach of Celtic, winning is the most important thing."
His success at Salzburg has resulted in Marsch being linked to top jobs in the German Bundesliga – it is thought he could be in line to take over Dortmund in the summer – but he is contracted to the Austrian club until the summer of 2022.
On the Celtic role, he added: "I know enough about it to say of course it's interesting. It's an amazing club and it would be an honour to even be considered. But I also have a job to do here.
"My way of working is really to focus in on the job that I'm doing and concentrate on the moment. And the more that I do that the more other possibilities can arise."