The Argentine coach has been linked with the French club for weeks and the vice-president insists they have reached a "tentative" agreement
The former Argentina, Chile and Athletic Bilbao coach has been linked to the Ligue 1 club for several weeks and it appears a contract is close to being finalised after Labrune's comments following Marseille's 0-0 draw at home to Lille on Sunday.
"We have a tentative agreement which is now subject to the drafting of contracts," he told reporters.
"Without falling into absolute euphoria, we can say that we are confident that this issue will be finalised ... I can say that we will have a great coach for next season."
Jose Anigo has been in charge of Marseille in a caretaker capacity since December last year, when Elie Baup was sacked.
Marseille are struggling in sixth in the Ligue 1 table and appear unlikely to qualify for European football for next season.