Marina Del Rey, Los Angeles. Roberto Mancini, in shorts and trainers, looks even more tanned than usual, the product of several weeks back home in Sardinia. The sun is shining here in California, too, and Mancini is already talking about wanting to return next year.

And yet it is clear there is something troubling him. This, in essence, is supposed to be the season when all that spending of Abu Dhabi's oil riches was meant to leave Manchester City in a genuine position to challenge for the prizes they covet the most. The remit was always to win the Premier League but it is a little shake of the head, a blowing of the cheeks, when Mancini is asked whether this is the point in the process when City can be considered potential champions in the making. "At the moment we are not ready to play for the title."

He qualifies this by pointing out that he may think differently in the coming weeks – if, that is, the club are able to lure Sergio Agüero from Atlético Madrid and find a way of persuading Arsène Wenger to part with Samir Nasri.

For now, though, this is a slightly downbeat Mancini, pensive even. Manchester United have already spent £50m this summer, after winning the league by nine points last season. City, in contrast, have adopted a new line of conservatism that is not entirely to the liking of their demanding manager.

"It's been difficult," he says. "United and Chelsea don't need to buy six players. They need only two or three and they are OK. But for us, it's different."

He wanted five, possibly six, new players, but has come to realise that will now not happen. "We have signed [Gaël] Clichy and [Stefan] Savic but we have also lost players as well, like Jérôme [Boateng], like [Patrick] Vieira."

The frustration is clear. "When you start pre-season you need the players [in place] because now is the only time you can work well with the players for three or four weeks." He made this point at the end of last season to the chief executive, Garry Cook, and the football administrator, Brian Marwood. The timescale has not been met and Mancini feels he "can be disappointed about this".

Could more have been done behind the scenes? "Always. For a team like us, it's important to move quickly, to move [for players] before the end of the season. If you move before, then you have no problem in June and July. You have the players for pre-season. If you don't, then you lose 20 or 30 days with them."

The backdrop to this is that, by his own admission, Mancini's relationship with Cook has been troubled at times over the past few months. This is the only time he has addressed the matter and his take on it is that "maybe we had a different way ... I think this way, and Garry another way, but this is normal when you work with other people. We have all the same targets – we want to win. All of us want to win."

He says there is a "good relationship" now but it is here, for the first time, that he also admits he wants more control within the club, over transfers, over the medical side, over player contracts and other issues.

Sir Alex Ferguson, after all, once said that a manager should have more control than anyone else at a football club. "I agree with him," Mancini says. "He has been at United for a long time so, for him, it is easy. Maybe, for me, it's difficult because I have been here only 18 months or so. But maybe I need to have more control of the other situations. It [the club] can improve that way. Maybe if I win the Premier League this season it will be different."

These could easily be construed as the early shots of a power struggle – or, at least, one that is potentially in the making. "It's very important," Mancini continues. "It's important for the manager to have control, over the players, the medical staff, the other situations. If the manager loses it's the manager who is sacked, so I think the manager needs to take every decision. If he makes a mistake, he pays for it."

They are comments that are unlikely to go down brilliantly at the Etihad Stadium, or in Abu Dhabi, where the club's chairman, Khaldoon al-Mubarak, is acutely aware of the occasional tensions between Mancini and Cook but has the attitude that all these matters should be kept behind closed curtains.

Mubarak summoned Mancini to Abu Dhabi at the end of last season to explain, alongside Cook, why the manager would not be given the financial backing of previous transfer windows. Mancini was irritated in the extreme and there was a feeling at the top of the club that the Italian was not fully taking into account the Uefa financial fair-play rules – though he says that is not true. "I know them very well. If these rules are in football we need to respect them."

What is clear is that the regulations have affected City more than any other club in Europe. In previous windows City would have happily paid over the odds for their main targets but when it came to Alexis Sánchez, newly of Barcelona, the new, more cautious City chose to pull out. "It was difficult [missing out on him]," Mancini says. "But the market is difficult. There were two or three other teams after him. We couldn't do it."

Agüero has now replaced Sanchez as Mancini's primary target. "He can score a lot of goals for us. Agüero, for me, will become a top striker. He is 23, he can play as a first striker or a second striker. He has good technique. He could play with Carlos [Tevez], or [Edin] Dzeko, or [Mario] Balotelli." Mancini is nodding to the sound of his own words. "I really think that now is his time."

He also thinks Dzeko and Balotelli will be better equipped for their second seasons in English football. "Dzeko improved a lot in the last two months of last season and Mario was the same. They will be OK. After a year in the Premier League they will have improved a lot. They are good players."

There will, however, be no reprieve for Craig Bellamy and it is here that Mancini demonstrates that, behind the smile, this is a man who budges for nobody. "We already have three strikers," he says. "I think it will be difficult to have a player who can play only once a month. I don't like this."

And Tevez? Where will he be when Swansea City arrive on 15 August? "Carlos is still a City player at the moment. He should fly back to Manchester at the start of August, before the Community Shield. He is still an important player for us."

It is difficult, however, for Mancini to be certain, especially as the Argentinian does not even return his manager's telephone calls.

Will Tevez play for City again? "Yes." But surely, after everything that has been said and done, not as club captain? Mancini smiles knowingly, as if he takes the point. But this time he says nothing.