United, who made the offer before Tito Vilanova resigned as coach owing to ill health on Friday, were privately given the same response as before – that the 26-year-old is "completely nontransferable".
The champions are weighing up whether to make what could be their final play for their No1 target in the region of £35m – surpassing the £30.75m they paid to sign Dimitar Berbatov from Tottenham Hotspur in 2008.
Barcelona have reached an agreement with Gerardo Martino for the Argentinian to take over from Vilanova and much may depend on whether the 50-year-old, whose coaching jobs have included Paraguay and, in his native country, Newell's Old Boys, will want Fábregas to remain at the Camp Nou and become a pivotal part of his plans.
David Moyes said that United could walk away if the deal drags on. Speaking in Tokyo on United's pre-season tour, the manager said that Ed Woodward, the club's executive vice-president, was dealing with negotiations. "My understanding is that Ed's had a response and he's spoken with them and again we've made a second offer," he said. "But Ed's dealing with that, rather than me personally here."
Asked if a stage can be reached where it becomes fruitless to continue, Moyes said: "I think a point does come but I think when you are interested in good players you want to give it every opportunity to materialise. And I'll do that. I'll hope that things can continue to move forward. At this moment I can only tell you that Ed Woodward is working hard to make the deals happen and we're hoping some of them will fall into place shortly."
Moyes accepted that the longer United go on without making any major signings this summer the more anxious fans become. "I can understand that but there isn't any real update I can give you. But I can understand why that might be the feeling," he said. "But I think everybody had thought this might be the summer – with there being quite a few changes, my new position, other managers at other clubs – that it might be that the transfers are later in the month. I think that was always the thought I had when I came into the job. And you've got to remember I only started the job on 1 July as well, so I've only been in this job for three weeks."
Moyes, who has been joined by Shinji Kagawa, Chris Smalling and Ashley Young in Tokyo, is clear that United must move on from Sir Alex Ferguson and enter the "David Moyes era". While always respectful of Ferguson, the manager is intent on writing his own history as he prepares United for their title defence.
That is why he brought in Steve Round, Phil Neville, Jimmy Lumsden and Chris Woods from Everton to join his backroom staff, he said, while embracing Ryan Giggs as player-coach. "I needed it to be the David Moyes era now and I had to take David Moyes' era and David Moyes' time so that meant me taking some of my own people," he said. "But I couldn't do it without the help of Ryan Giggs. Phil Neville had known a little bit at both clubs. But more importantly he probably knew how I worked at Everton more than Manchester United." He was young – him and Ryan are young, its really important in this job that you also keep young, open-minded thoughts because you don't want to get too old in your ways."
Moyes underlined his desire to succeed when it was put to him that he may need six months or even a season for the side to become his. "It is my team now. I have taken over, I'm in charge," he said. "As I have said, I will use the ex-manager as much as I can because of his knowledge but it is my team now and I have to take responsibility for that. From day one, it is my team and I have to get on and show that."
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