Ings is out of contract with the Premier League side at the end of the season and is now free to negotiate with interested clubs.
Moyes is reported to be keen on signing the 22-year-old, who could join La Real for little more than ??200,000 next summer, but the Scot would not confirm or deny his interest in the forward.
“I can’t comment on individual players because I don’t want to destabilise my club or another club, but I do know that Loren (Juarros, sporting director) and Jokin (Aperribay, club president) are working very hard to bring in players,” Moyes told a press conference, broadcast on the club’s official website.
“We’ve only got two weeks left and we’re working hard to try to get players in. It’s not an easy market, (but) we’re still hopeful by the end of January we can do so.”
Ings has scored six goals in 18 league starts for Burnley this season. La Real’s top scorer Carlos Vela has been responsible for over a third of his side’s 19 league goals, finding the net seven times in 14 starts.
Sociedad were knocked out of the Copa del Rey on Wednesday, their 2-2 draw with Villarreal not enough to overturn a 1-0 deficit from the first leg, but they have a chance to redeem themselves at home to Rayo Vallecano on Saturday.
Paco Jemez’s side were beaten at home by struggling Cordoba on Sunday, but Moyes still had plenty of praise for the Vallecas outfit, who won 3-2 at Anoeta last season.
“I’ve seen Rayo play. They have a very open style of play, so it will be a different type of game to what we’re used to,” he said.
“We’ll have to defend well and be patient about winning the ball back. The players know Rayo well and they are prepared for the match.”
Moyes also confirmed Carlos Martinez would miss the game through injury, and said David Zurutuza and Joseba Zaldua were doubtful despite returning to training during the week.
Rayo, meanwhile, will be without their talisman Leo Baptistao through injury, but defenders Antonio Amaya, Emiliano Insua and Ze Castro return after missing the defeat to Cordoba.