Speaking to BBC Radio Scotland programme Sportsound, the 47-year-old revealed that Celtic’s links with former club New York Red Bulls had led to the Parkhead side sponsoring him so he could complete a coaching course in Scotland.
But despite admitting interest in the role, he stressed his full focus was on finishing the current season with his current club.
Marsch said: “I wanted to further my education as well as trying to qualify myself to be a coach in Europe.
"I took my badges in the US but I needed to be educated in Europe. Red Bulls had a relationship with Celtic, and Celtic sponsored me to be on the course, which I took from 2018 to the end of 2019.
"It was very difficult and very stressful; I had to often fly over on a Saturday night directly after our game on a red-eye, then go straight from the airport to the course that lasted eight or nine hours that day, then get a little bit of sleep that night, then wake up on the Monday and go through the course again and sometimes on Tuesday as well, then fly back and coach my team. I did that probably 15 times.”
Explaining the differences between doing his badges in Scotland and in the US, he added: "What I learned – not just about Scottish football – but Scottish people, is how welcoming they were, how open they were to the ideas I had, how challenging the course was.
"Jack Ross was on the course with me and I thought he was really good, [former Hamilton boss] Martin Canning too. A lot of the assistant coaches in the league and some that are starting to be head coaches."
Marsch’s success in New York and now in Austria is gaining him admirers, with Borussia Dortmund said to be keen on his services. But the Wisconsin-born manager isn’t getting carried away.
"Right now my full concentration is on finishing my year here in Salzburg. Then, I'll evaluate in the summer what the possibilities might be for a potential next step,” he added.