Last year, it emerged that Hewer has been installed as the new host of the Channel 4 game show following the departure of presenter Jeff Stelling.
Hewer has now quipped that he can see Mountford, with whom he previously worked on The Apprentice, making an appearance on the show.
"I may well wrestle her into Dictionary Corner," he said, according to The Sun. "She's busy studying but if I were a betting man I'd put a fiver on it."
Hewer, who has previously admitted that he was nervous about taking on the Countdown job, also revealed that he has faced some problems hosting the show.
"I spotted a good word among the letters and shouted out, 'Conifers'," he said. "It ruined the shot and filming was stopped."
Countdown will return with Nick Hewer as the host on Monday on Channel 4.