United have had two bids for the Spain international turned down already but Moyes insists they have not given up hope of landing the former Arsenal man.
Asked about the potential deal at a Thursday press conference as United continue their tour of Japan, Moyes said: "It is ongoing."
And the new United boss also said that forward Robin van Persie is likely to feature in Friday's friendly against Cerezo Osaka.
Van Persie felt tightness in his thigh during Tuesday's loss in Yokohama and had to be taken off.
Van Persie expected to play
But Moyes said: "It was just a precaution. I expect he will play tomorrow."
However, Michael Carrick is unlikely to be risked on Friday, although Moyes says the midfielder's tight groin is getting better.
Regarding injured players who are rehabilitating back in Manchester, the manager said the news was good.
"There was a practice match at the training ground the other day in which Nemanja Vidic, Antonio Valencia and Nani all got some playing time," he said.
"Wayne Rooney is running and is probably at the level we would have thought he would be at. He has picked up his work again this week."
Meanwhile, Alex Song is convinced Fabregas will still be a Barcelona player at the start of the new season.
Song, the former Arsenal midfielder who spent six years at the Emirates before moving to Spain in 2012, says his team-mate has no intention of quitting Camp Nou.
After featuring in Barca's friendly defeat at Bayern Munich, Song told Sky Sports News he is "100%" sure Fabregas is going nowhere.
He said: "I did not speak with him but I know Cesc is 100 per cent here.
"He loves Barcelona, he loves the club. He will stay here next season and give 100 per cent because I know him very well and he'll want to fight. He's focused on the club.
"He wants just to give his best for Barcelona. He's from Barcelona, he loves Barcelona and he'll want to start the season to show what he can do.
"People are talking and talking, but we know he is focused here and ready to start the season.
"He's enjoying a holiday with his family and I'm sure he wants just to come back here.
"It's my own opinion but I know he will stay here, 100 per cent."