The Black Cats boss has reportedly made a bid for Norwich City midfielder Robbie Brady.
Moyes would not name names but confirmed the Premier League relegation fighters are actively looking for new talent.
“We are trying, always pushing, always hopeful,” said Moyes, who saw his FA Cup hopes end last night with a 2-0 defeat at Burnley in their third-round replay.
“We’ll need to see what happens. It’s more than someone we need, that’s obvious.”
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There has been speculation that Sunderland have made a £10million offer for Brady, but Moyes was playing his cards close to his chest.
“I will not talk about players at other clubs, I don’t think that’s fair,” said the Scot. “But what I’ll say is that we have tried to do one or two things.”
At 24, Brady is an ideal age, and he looked good in the Premier League with Norwich last season and impressed in the Euros in the summer in France.
The gifted Republic of Ireland international could prove a great signing, should Sunderland pull it off.
His squad is currently at breaking point with midfield particularly hard hit with Lee Cattermole and Jan Kirchhoff as long-term absentees, with Steven Pienaar (calf) now joined on the sidelines by Jack Rodwell (knee).
With record signing Didier Ndong away at the Africa Cup of Nations, it means Sunderland are down in terms of quality and quantity.
It was felt Moyes would have to sell before he could buy given the club’s colossal debt and high wage bill.
But the manager appears to be being backed in the market by owner Ellis Short.
“Everyone knows our limitations in what we can and can’t do,” said Moyes. “We are needing to add because of our shortage [of players].
“We have one or two players who are quite close but we have long-term absentees and boys away at the Africa Cup of Nations.”
Sunderland’s limitations on the field were exposed by Burnley who scored a goal late in each half.
But Moyes does not see a Saturday or two off in the coming weeks as being a help during the relegation struggle.
“No I didn’t want any free weekends,” he said.
“I don’t mind free weeks so we can train through the week but we wanted a run in the cup.
“I think our big chance came at the Stadium of Light, but I still felt we could be good enough to beat Burnley.”