The Black Cats are desperately trying to bolster their wafer-thin squad ahead of Tuesday's transfer deadline with Moyes looking to a number of his former players to help lift the club from the foot of the table.
Last week, Joleon Lescott became the latest man to have played under the Scot to arrive at the Stadium of Light with Gibson and Oviedo now expected to sign up in the coming hours.
"It's going well," Moyes told at a press conference ahead of the visit of Mauricio Pochettino's side. "Hopefully in the next hour or two we'll be able to confirm. Not done yet."
With Victor Anichebe, another of Moyes' former players from his spell in charge at Goodison Park, sidelined until possibly April with a knee injury, Sunderland are also in need of another centre forward to ease the goal-scoring burden on Jermain Defoe.
The club are now looking into the possibility of signing Leicester City striker Leonardo Ulloa, whose agent recently told IBTimes UK the player "doesn't want to be at a club that doesn't want him."
According to Sky Sports, Leicester have already rejected a £3m offer from Sunderland for the Spaniard, with Moyes unwilling to discuss the club's attempts to bring him to Wearside.
"I very rarely talk about players from other clubs until the time is right."
Patrick van Aanholt's £14m move to Crystal Palace, where he will be reunited with Sam Allardyce, leaves a spot vacant at left-back in Moyes' starting XI. While the expected arrival of Oviedo will fill that role, Moyes suggests the club could bring in two players to cover the position for the remainder of the season.
"We'd like to get ourselves a left-back. We made our position clear before January, but we are trying to add one or two."