The pair are on Wearside to finalise their moves from Everton.
And ahead of tomorrow night's clash with Tottenham, Moyes expressed confidence that both will be complete before the transfer deadline.
Sunderland transfers: Deadline day rumours rated
Mon, January 30, 2017
Football Whispers have rated Sunderland's chances in the transfer market ahead of deadline day (1 – unlikely, 5 – likely)
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Football Whispers have rated Sunderland's transfer chances (out of 5)
Bryan Ovidedo asked to leave Everton
He said: "It's going well. Hopefully in the next hour or two we'll be able to confirm, but they're not done yet."
Earlier Everton manager Ronald Koeman explained he agreed to let Oviedo leave after talks with the player.
Darron Gibson has fallen out of favour with Ronald Koeman
He said: "With Oviedo it was difficult. He is the back-up for Leighton Baines. He is a perfect professional. He wants a new challenge to play at Sunderland.
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"I had told him no way, no chance, but I changed my mind. I don't know if it's the best solution but I like the boy, he was working hard and he wanted to play.
"If we get a problem at that position we have some good young ones."