The midfielder, signed for a reported £3m from Huesca in July, marked his first appearance in England with a hat-trick to hand Leeds a 4-1 win over Vale in the EFL Cup.
Brown has since claimed that Saiz spat in the face of Vale defender Joe Davis shortly before half time, before going on to score his second and third goals of the game in the second half.
The Valiants boss also claimed that he had asked Leeds to take Saiz off at half time following the alleged incident, but the Yorkshire club have now come out in support of their player.
"We are disappointed by allegations made following our game with Port Vale last night, we are also disappointed by the treatment of our players throughout the match," a Leeds spokesperson said.
"Our player denies the allegation and we are confident that the referee's report will vindicate him."
The Football Association is aware of the allegation and is investigating the incident.