The two firms have challenged before the tribunal Mistry's removal from the Tata Sons last year.
The bench of B S V Prakash Kumar and V Nallasenapathy is likely to pass the order on April 17.
The two Mistry family companies urged the NCLT to waive the condition that a petitioner before the tribunal should hold at least one-tenth of the issued share capital of the company or represent at least one-tenth of its minority shareholders.
The petitioners said that NCLT can use its discretion, granted under the Companies Act, to waive the condition.
Tata Sons argued that if preference capital is also considered, the two petitioner firms hold only 2.17 per cent of the total issued share capital of Tata Sons, and hence they could not move the NCLT.