The Teesiders are believed to have upped their offer to £1.5m.
Leeds have already rejected two bids of £1m and £1.3m over the last month.
McCormack underlined his value to Leeds with a stunning individual goal in the 1-1 draw with Sheffield Wednesday last Saturday.
But Boro boss Tony Mowbray is a big admirer of the Scottish international while Brian McDermott has admitted recently that he needs to cut the wage bill and has to sell players before he can buy.