Ncube is supposed to replace Arthur Mutambara as the second DPM after he dislodged the robotics professor at the helm of the party last month.
But Mugabe has indicated that he would not force Mutambara to resign if he does not want to.
State media last Friday reported that Mutambara had already told Mugabe that he was not going anywhere.
Ncube on Saturday said he would meet Mugabe this week, probably on Tuesday, to brief him on his party’s position, which means Mutambara would be demoted to Regional Integration and International Cooperation minister.
“I have made a request to talk to the president. We will most likely meet this week on Tuesday,” he said.
“We don’t believe he will refuse once we put it to him.”
The DPM designate said MDC would not allow any other party to choose a principal for it, in the clearest indication yet that the formation is prepared to leave the unity government if Mugabe sides with Mutambara.
“We think that to refuse to recognise a representative of our party will be basically destroying the foundation of the government of national unity (GNU).
“The GNU is a three-party coalition represented by people of each party’s choice. Once we have people chosen by other parties it destroys the foundation of the GNU.
“We trust that no one can possibly suggest who our representative should be,” Ncube said.
Mutambara has not commented publicly about his response to the MDC’s decision to demote him.
He has been out of the country since the decision was made and is expected back home this week. Ncube said he had not spoken to his predecessor about the matter.