United pressing ahead with Cesc bid
United have had two bids for the Spaini nternational turned down already but Moyes says 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 confirmed Robin van Persie will play some part in Friday's friendly with Cerezo Osaka.
Van Persie was taken off as a precaution during Tuesday's defeat in Yokohama after feeling tightness in his thigh.
The injury prompted a stinging attack from former Wales coach Raymond Verheijen, who recalling Moyes' previous claim he had "overtrained" Van Persie during United's week in Australia, said such training regimes were out of Jurassic Park.
It seems the comments were overblown, with Van Persie set to play in the fourth match of United's pre-season tour.
"It was just a precaution," said Moyes. "I expect he will play tomorrow."
Moyes confirmed Michael Carrick's tight groin was getting easier but the midfielder is unlikely to be risked.
And there was good news surrounding four of the players United opted to leave at home.
"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. He has picked up his work again this week."
With conditions in Osaka even hotter than Yokohama, Moyes is set to abandon his policy of giving players extended periods of time on the pitch in an effort to conserve their energy.
"It's very hot and the conditions are difficult for players from our country," said Moyes. "I hope we'll benefit from playing in these conditions when we get home but we may need to use all of our players tomorrow night to make sure they don't lose too much weight or fluid because I am sure it will be very hot again."
With two defeats from three games it has not exactly been the best of tours results-wise for Moyes as yet.
However, the form of Jesse Lingard, currently top scorer with three, and Adnan Januzaj has caught the eye.
And rather than send them out on loan, which had been established policy under Sir Alex Ferguson, Moyes is considering whether to keep them at Old Trafford to allow them to continue their development.
"Both have done well," said Moyes. "They have adapted well and made contributions to the team. It's a tradition at United to try and get young players into the team and both have come through the system. Hopefully we can get both some playing time next season but both need to keep their levels up and keep making an impact in training and games."