The former Spain midfielder is out of contract on the south coast and his performances towards the end of last season alerted a host of clubs in England and abroad.
But Poyet has given his clearest indication yet that he believes 30-year-old Vicente is ready to commit his future to the Seagulls.
"I think Vicente will stay," Poyet told the Argus.
"What we are trying to do is sort out a few little things that will make sure he is staying with us, in a better and happier situation with us, but I think it will happen at any time.
"We are just trying to sort it out. We cannot confirm if he is going to stay or not because that's not fair. We cannot do something that isn't done but I would say it is a big chance, 90 per cent or 95 per cent that he will stay."