Daniel James’ imminent arrival from Manchester United has raised concerns about the 27-year-old’s future at Elland Road.
With uncertainty regarding his future in the team, Costa has been linked with a deadline day move away from the Yorkshire-based club.
La Liga club Valencia are said to have enquired about the possibility of signing the winger, with Leeds prepared to sanction a loan move for him.
However, according to Spanish radio station Tribuna Deportiva, Valencia boss Bordalas has blocked a potential loan move for Costa.
Both Leeds and Costa are open to the idea of joining the Spanish top flight club on a temporary deal, but the Valencia coach is not keen on the move.
Costa’s agent Jorge Mendes has also been trying to get a deal over the line, though Bordalas has now put an end to it.
With a move to Valencia blocked by Bordalas, it remains to be seen where the immediate future lies for the former Wolves star.