Bridge is currently on a season-long loan from Manchester City after finding himself out of favour at the Etihad Stadium.
The former England international has impressed since his arrival at Brighton and has been an ever-present for Poyet's side in the Championship.
Poyet would love to keep the left-back at the club, but concedes it is too early to consider extending his contract with the player set to become a free agent next summer.
"From the club point of view, it's very easy. From Wayne's it's very difficult," admitted Poyet.
"We are trying to be realistic and wait. At the right time we will talk for sure because you can see he is different class.
"When the right time comes, slowly, we will probably get close to [whether Wayne staying is] a possibility or not.
"I think it's a bit too early, especially for him.
"If I was him, it's not a problem to ask the question or start talking.
"But I don't want to put Wayne in a difficult situation and him say 'Not now' and maybe people will think he won't be here."