The arrival of Daniel James from Manchester United opened up the possibility of a loan move for Costa in the final hours of the transfer window.
Sheffield United, as well as clubs in Spain and Turkey, were interested in signing the 27-year-old, but Valencia appear to have won the race for him.
Leeds and Valencia are claimed to have reached an agreement over the loan transfer of the former Wolves star just in time.
According to Spanish radio station Tribuna Deportiva, the Whites will pay a portion of Costa’s wages during his time on loan at Valencia.
The winger is said to be earning €3m per year at Elland Road and Leeds will continue to pay half of it during his time away.
There have been suggestions that Leeds want a loan fee to sanction Costa’s move to Valencia, but it remains to be seen if they are receiving a sum.
Valencia have been claimed to want an option to make the move permanent in their agreement with Leeds and it is unclear whether the Whites were prepared to agree to that.
