The Argentine coach's future at Stade Velodrome is in doubt, despite Marseille having provided a sustained challenge for the Ligue 1 title this season.
Sunday's 1-0 defeat at Bordeaux left Marseille a place and a point off third-place Monaco, who are in the final UEFA Champions League position.
Bielsa has previously been coy about his future beyond this term, with his contract including a termination clause after one year.
However, Bielsa explained: "She [Louis-Dreyfus] told me she wanted me to continue here.
"She told she something that I really enjoyed - that she loved what I was doing on a human level, in my attitude and the way I lead the squad.
"I shall try and live up to Margarita Louis-Dreyfus' high praise, I would dearly love to finish the season second or third."
However, Bielsa added that he had not been offered a concrete deal to stay, saying: "Asking me not to leave is not the same as offering me a new contract."
"We coaches know and understand that when we fail to achieve our objectives there is a price to pay."
