David Moyes and his squad flew back to England immediately after Manchester United's 5-2 win over Kitchee FC, with the manager set for urgent discussions with the club's executive vice-chairman, Ed Woodward, regarding the pursuit of Cesc Fábregas – as it was also claimed that Nani has been "offered" to Monaco.

With United yet to make a major signing this summer, Moyes's first business in the transfer market may involve losing a player rather than acquiring one.

Monaco's sporting director, Vadim Vasilyev, claimed in the French newspaper L'Equipe that the Portuguese winger, who was not on the tour because of a nose operation, "has been offered to us".

Vasilyev added: "He is a very good player but at the moment there have been no talks. We have already changed our group quite a bit and we also want to offer opportunities to our young players." Nani has only a year left on his contract and Moyes is yet to have the chance to assess his worth, which will happen when the squad return to their Carrington training base this week.

Regarding Fábregas, Woodward flew back to Europe early from Sydney during the second leg of the tour, with the pursuit of Fábregas high on his agenda. With Moyes leading the squad on the 21-day trip, this week will be a first chance for the manager to give the potential purchase of Fábregas his complete focus.

Following the win over Kitchee in United's final pre-season tour game, Moyes was asked if Woodward had made any progress on Fábregas. "No. I've got no other updates to report just now," he said. With Barcelona rejecting £26m and £30m bids and stating categorically that the former Arsenal captain is not for sale whatever the price, Moyes is taking encouragement from the knowledge that Fábregas is open to the move.

Moyes and Woodward will consider whether to make a third bid, which is likely to be in the region of £35m, while Fábregas also has the option of putting in an official transfer request to try to force his way out of the club. But, given that Barcelona are his boyhood team, that is not thought to be a ploy he is likely to utilise.

The French club Monaco have claimed that they were offered the chance to sign Nani from Manchester United. Photograph: Tom Jenkins for the Guardian

The goalkeeper David De Gea has an injured finger that could make him a doubt for United's next friendly, the trip to AIK in Stockholm on 6 August, and he was rested for the game against Kitchee.

"David De Gea has got a finger [problem], so we just didn't risk him in the last games," said the manager, who a month into succeeding Sir Alex Ferguson is beginning to settle in.

"I'm a bit more relaxed because of being around the players and them getting to know me and I think they'll feel a wee bit the same way, a new manager coming in, and I've enjoyed being with them," he said. "They've been really good to work with and I think the work we've asked them to do has been very good.

"They were already very good players. I'm just taking on the baton and keeping it going, if I can.

"This was going to be a daunting job for anyone who takes it. For whoever was going to replace Sir Alex it was going to be a hard task. So it was always going to be daunting but certainly you grow into it and, as the days go on, you start to feel a bit more comfortable."

After stops in Bangkok, Sydney, Tokyo, Osaka and Hong Kong Moyes conceded that the tour was not the best preparation for the title defence. "I don't know if it would be ideal preparation. I don't think it is what every team would certainly choose," he said.

"I think in football now if you're one of the big clubs, you have to take your club to the supporters around the world. It means the extra money you earn from your marketing and from your sponsors is going to play a big part in the future. So I think it's something we're going to have to come to terms with and it is going to happen – and maybe even more so in the future."

Moyes also stated that letting in nine goals in the five tour matches is a worry. "We're concerned about conceding the goals," he said. "But I think United were a bit like that at the start of last season and what they tended to do was score more than the opposition."