The Sunderland boss is hopeful the striker will be well enough to return to Wearside with the squad after collapsing during the interval in the 2-2 draw with Cardiff City
The Premier League's bottom club produced a stirring fightback as a Steven Fletcher strike and a 95th-minute goal from Jack Colback earned a point for the visitors after Jordon Mutch and Fraizer Campbell had seemingly put Cardiff in command.
However, there is some concern over on-loan Liverpool striker Borini, who was replaced by Fletcher on Saturday after reportedly collapsing during the interval.
Borini had felt unwell in the build-up to the game and Poyet has since allayed fears over the 22-year-old by revealing he has now been released following his precautionary trip to hospital.
"He's in hospital now," Poyet told Sky Sports. "Fabio was feeling very bad before the game. Just before the game he was sick.
"We decided together, the players they want [me] to play him, then at half-time it was impossible for him, and now to make sure that everything is alright we took him to hospital so let's hope it's nothing and he can go back on the plane now up to the north."