While the brand has revealed no shortlist for who will replace the disgraced designer - sacked after being charged with racially abusing people in a Paris cafe - it is claimed that Marc is top of the list for Bernard Arnault, chairman of LHVH, the parent company of Dior.
A source told Brazilian website Glamurama: "The two have met often in recent weeks to discuss the matter.
"Jacobs, the current creative director of Louis Vuitton, renewed his contract with LVMH in January - and it is possible for him to continue in his current position even if he takes over Dior."
Fashion insiders find it highly unlikely, however, that Marc would direct both brands.
The source added: "More likely, however, is that he'll end up choosing between one of two. Arnault would prefer him to go to Dior - as the billionaire sees it; Jacobs' image will only be good for The Fashion house, which was considerably shaken by the Galliano scandal."
Marc has previously denied, that he was in the frame for the job earlier this year, saying: "I haven't been asked."
LHVM declined to comment on the matter when contacted.