Poyet is in the first season of a five-year contract at Brighton, but has in recent days been strongly linked with the vacant Wolves managerial role.
Oatway told The Argus: “In my time at Brighton we’ve had some good managers linked with other clubs and they have gone on to so-called bigger and better things, so we are quite used to it, the fans and everyone.
“Nobody is surprised Gus is getting linked with other jobs and that includes us, the chairman and his board of directors and the fans. It’s one of those things that is going to happen.
“Gus has signed a five-year contract with a bigger picture and a bigger plan with the chairman to build this club through the right avenues and I am sure they will.”