Marsch, whose last job was as head coach of RB Leipzig, is set to be unveiled on Monday.
Bielsa's Elland Road exit was confirmed on Sunday almost 24 hours after a 4-0 defeat at the hands of Tottenham Hotspur.
The defeat, which followed a 6-0 loss to Liverpool in midweek, means the Whites have just two wins in their last 11 Premier League games.
Leeds now sit 16th in the Premier League table with 12 matches left to play but just two points clear of the relegation zone.
Marsch left his post at RB Leipzig on December 5 after just 21 matches in charge of the Bundesliga side.
A replacement for Julian Nagelsmann, who had left for Bayern Munich, Marsch was unable to make the necessary impact and even oversaw a 6-3 loss to Man City in the Champions League before his exit.
Prior to the role in Germany, the 48-year-old had won two titles in Austria with Red Bull Salzburg
And previously, after spells with Montreal Impact and New York Red Bulls, Marsch had been assistant coach to current Manchester United interim manager Ralf Rangnick.
He was also assistant manager to Bob Bradley with United States at World Cup 2010 where they reached the last-16.