Boro had a third bid of £1.5million rejected over the weekend and they returned with a fourth bid on Wednesday - which Sky Sports understands has been described as their 'final offer' for the Scottish international.
Leeds are now considering their position although it is thought Boro want a decision before the weekend or they will move on to other targets.
McCormack remains Tony Mowbray's first choice, and Boro are hopeful that £2million will be enough to get him.
McCormack has stated that he is happy at Leeds, but if they decide to sell then he would accept their decision.
Boro are hopeful of concluding a couple of deals in the coming days, and they are also holding talks with Norwich City over defender Daniel Ayala.
The former Liverpool defender could now be set for a loan move to The Riverside, with a view to a permanent switch.