Red Bull-owned AlphaTauri said on Wednesday that Franz Tost will be stepping down as principal at the end of the 2023 season with Mekies arriving to replace him at a date to be confirmed.
He was the second senior team member to head for the exit since Mattia Binotto was replaced by Frenchman Vasseur in January.
David Sanchez left in March and is due to join McLaren in a senior technical role next January.
"I think it’s a mega opportunity for Laurent," Vasseur told reporters at the Azerbaijan Grand Prix in Baku. "I won’t block Laurent, for sure.
"If you speak about timeline, I think that Toro Rosso (AlphaTauri) was probably a bit aggressive on the press release. We have a long-term contract with Laurent and we’ll have to discuss about details."
Vasseur said he had a good relationship with Mekies and they had open discussions but he would always put Ferrari's best interests first.
"To lose two people in 1,600, it’s not a drama," he added. "The power of the team is always more important than the individuals.
"The group is there, we are recruiting massively - that we are not communicating but we are recruiting massively - and we will do step by step.
"You know perfectly the system of recruitment in F1, it's quite long and painful but we are working on it."
Vasseur recognised Mekies' current role was 'quite large" and said it could ultimately be split in two, as some other teams have done.
The Frenchman also said Charles Leclerc (25) remained a central part of the Ferrari project, amid media reports the Monegasque could be looking elsewhere with a contract that expires at the end of 2024.
