The pitch follows the arrival of new comms head Andrew McConnell in the spring, and comes as the airline recovers from the financial troubles that have plagued it since the credit crunch.
It posted an £8m profit for last year following a major restructure in that saw staff numbers cut by more than 1,000.
Flybe also has a new CEO, Saad Hammad, who joined from easyJet in 2013.
Instinctif, known as College Group when it was appointed in 2004, has been invited to compete for the work, with the process understood to be at pitch stage.
McConnell, who also joined from easyJet, said: "We can confirm that we are in the process of engaging with a number of PR agencies, including the incumbent, as part of a routine review of our corporate and financial PR agency services. This approach is consistent with our corporate governance processes."
Instinctif declined to comment.