The Whites are understandably reluctant to part with their in-form Scotland international and have knocked back all bids put on the table.
Mowbray is refusing to concede defeat in the protracted chase, though, and could make a fresh approach before the summer window closes.
Whether he can tempt Leeds into a sale remains to be seen, but the Boro boss will be pushing to get deals over the line before 2nd September.
He told the Gazette: "I'm loathe to mention individuals, but McCormack is a player we have enquired about.
"I think it is three in three he has scored now for them and he is a fans' favourite.
"It might be difficult for them to sell him, but we can only ask the question of clubs.
"I don't think it's over. Look at the bigger clubs - is the Rooney issue over, is the Suarez issue over?
"Once the window shuts, he won't be signing. But I've got total respect for the club the boy is playing for and he is doing pretty well for them."
He added: "I still think we need three or four more players. It's proving more difficult than we might have hoped but we aren't the only team in English football not being able to put that jigsaw puzzle together.
"The conundrum for us is not rushing in and getting players who don't necessarily fit with what we are trying to do."