The venerated Argentine has enjoyed large swathes of admiration from the Leeds supporters for his role in getting them promoted back to the Premier League.
His success continued in the Premier League with a top-half finish last term, but this season has not gone according to plan for the Whites, with relegation not entirely out of the picture.
As is customary with Bielsa, he is on a season-by-season contract and it is a possibility the boss steps down from his job in the summer.
Marsch has emerged as the candidate most favoured by the Leeds hierarchy should the scenario arise that Bielsa leaves after the season is over.
Former Barcelona coach Ernesto Valverde and current Huddersfield Town boss Carlos Corberan are also in the running, but Marsch is liked best.
Leeds may have a competitor on their hands though as La Liga club Athletic Bilbao could make a move for Marsch depending upon the situation in the summer.
Marsch was fired midway through the season at RB Leipzig after a less-than-stellar campaign, but enjoyed much more success at their sister club Red Bull Salzburg.
