Prior to the recent Azerbaijan Grand Prix, it was confirmed that current Ferrari sporting director Mekies is to replace Franz Tost as team principal next year.
Mekies, however, has a long-term contract with the Scuderia, with negotiations ongoing as AlphaTauri seek to avoid him being placed on a lengthy period of gardening leave.
Horner has indicated, however, they are only at a junior level and so do not carry the necessary weight for an exchange to take place.
Asked about the matter ahead of this weekend's Miami Grand Prix, Horner said: “Again, as usual, there's plenty of speculation.
“Will there be a hostage exchange for Laurent Mekies? Well, we don't have any hostages.
“So, in terms of personnel moving to Ferrari, certainly at a senior or medium level, there's nothing planned.”
Speculation had surfaced that two members of Red Bull who could be on their way to Ferrari were technical director Pierre Wache and aerodynamics chief Enrico Balbo.
Horner, however, has indicated there is no truth to such rumours, particularly after speaking with the staff concerned.
“Individuals that have been mentioned in connection with Ferrari came to see me last week and mentioned their disbelief in some of these rumours,” said Horner.
“But it's Formula 1. That will inevitably happen, but there are no plans for any senior members of our team to be joining Maranello.”