United boss Brian McDermott said after his side's derby draw with Sheffield Wednesday at the weekend that the club had rejected "two or three" earlier bids from Boro for the former Cardiff striker.
McCormack struck a fine solo goal to earn Leeds a point on Saturday and Boro duly returned with a further improved offer believed to be in excess of B£1.5million for the Scotland international on Tuesday, which has also been dismissed.
It is understood that Leeds want to open talks with McCormack's agent over an improved deal. He is currently 12 months into a three-year contract he signed last summer.
Leeds have made no secret of their desire to reduce the wage bill at Elland Road, but McCormack is not one of the players they want to move on and the Scot himself told reporters at the weekend that he wants to stay.
"If I'm going to go, it's going to be their (the club's) decision," McCormack said.
"It's not going to be my decision.
"Not once have I asked for a transfer and I won't force through a move. But if there's an issue with the club and they need me to move on for money, sometimes in life you do things that you don't want to do.
"I'm firmly happy here and I'm settled in the area. It's always nice when other clubs are putting in offers for you but as I've said numerous times, I'm happy.
"This is a massive club and I'm really honoured to be here."