GOAL - by Peter McVitie
The German side want the American to take charge this summer after it was confirmed current coach Julian Nagelsmann will join Bayern Munich at the end of the season.
Leipzig have already settled on who they want to replace Nagelsmann and are negotiating with their sister club.
What has been said?
Salzburg spokesman Christian Kircher confirmed on Wednesday that talks have begun.
He told SID. "I can confirm that talks with Leipzig have been started."
It has been reported by German outlet Kicker that the Bundesliga side and Marsch have already reached a personal agreement.
Marsch wants Leipzig return
Marsch spent a year as assistant coach to Ralf Rangnick at Leipzig before moving to Salzburg in 2019.
The 47-year-old's contract runs until 2022, but he recently admitted that he would like to take the Leipzig job.
"Of course I understand the club very well. If you ask me what would fit best, RB Leipzig is of course a top idea," he told Sky.
Marsch was also recently linked with Eintracht Frankfurt, Tottenham and Celtic.