AlphaTauri announced ahead of the Azerbaijan Grand Prix that it has signed Mekies as its new team principal replacing Franz Tost, who will stand down at the end of this season.
However, no date has been set for Mekies' arrival at the Faenza-based squad because he remains under a long-term contract at Ferrari.
Tost suggested that the exact timing was something that would need to be sorted out between Ferrari and Red Bull.
"First of all, it's between Laurent and Fred [Vasseur]," said Tost about the process of sorting Mekies' arrival.
"Then, of course, Red Bull will take a major role in this. I think that Oliver Mintzlaff [Red Bull CEO] will then talk to the CEO from Ferrari and find a solution."
While Ferrari does not want to block the move entirely, team boss Fred Vasseur's annoyance at the timing of the AlphaTauri announcement has made him reluctant to bend over backwards to accommodate the switch as swiftly as his rival would like.
Speaking at the Azerbaijan GP last weekend, Vasseur said AlphaTauri's call to go public with the Mekies move was "aggressive".
However, Motorsport.com has learned that, with negotiations set to open up between Red Bull and Ferrari over the situation, key to it could be a compromise arrangement that suits both parties.
It is understood that Ferrari has been on a recent recruitment drive to lure personnel – including aerodynamicists - from other teams including several from Red Bull.
But despite deals being in place, Ferrari cannot get hold of these individuals for a while because of mandatory gardening leave periods.
However, sources have indicated that Ferrari may be willing to get the ball rolling on Mekies' departure to AlphaTauri if Red Bull agrees to an early release from the contract of its staff who are moving to the Maranello squad.
While Ferrari has not commented on the matter, Vasseur's close friend Toto Wolff has suggested that the Frenchman is ready to get aggressive in his dealings over the matter.
Speaking about the Mekies situation, Wolff said: "Fred needs to put his own team in place and take the right decisions.
"You can't stop a traveller. That was always my philosophy, that if somebody wants to go and sees another opportunity, let him go and wish him all the best.
"Fred is an out-and-out racer and knows exactly what he wants. I think he's okay with the situation, but obviously, the way it was communicated was a bit abrupt. That's why Fred's is going to do the best for Ferrari. And if that means taking the elbows out, then that is good."
