The Red Devils have made two offers for Fabregas, the second of which was reportedly £30 million. Both were rejected by Barcelona, and president Sandro Rosell has apparently written to United to insist that the player is not for sale.
It is believed that United are now weighing up whether to make a third and final offer in the region of £35m.
When asked about the transfer negotiations at a press conference in Japan, Moyes reiterated his desire to bring Fabregas to the club and said the situation is "ongoing."
United are in the country ahead of a friendly match against Cerezo Osaka on Friday.
The 26-year-old Fabregas is thought to be Moyes's top target as he looks for a marquee signing to herald a new era at Old Trafford.
Despite being linked with a host of big names, Moyes' only signing to date is Uruguay U20 defender Guillermo Varela.
Thiago Alcantara was heavily linked but opted to join former Barcelona boss Pep Guardiola at Bayern Munich while links with Cristiano Ronaldo, Gareth Bale, Everton duo Leighton Baines and Marouane Fellaini, plus Newcastle's Yohan Cabaye as yet have failed to bear fruit.
Moyes 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 a 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 he 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."