The Baggies boss left Greening out of the side which beat Peterborough on Tuesday night as negotiations between the two clubs continued and a deal now looks to be close.
"Basically the two clubs are negotiating," Di Matteo told the club's official website. "His team-mates are fighting for a cause. I didn't feel it was right for him to be involved last night.
"He's been a great professional for us. I spoke to him before the game. There has been a lot going on for him in the last five or six weeks but, once again, I have to emphasise he's been very good for us.
"He's been a true professional and it was my decision to pull him out last night."