Xabi Alonso has spoken with Enzo Fernandez and wants the Chelsea vice-captain to stay for next season despite the 25-year-old Argentinian appearing interested in a summer switch.

Alonso was unveiled in the Drake Suite at Stamford Bridge on Monday afternoon after starting work on his four-year contract. One of the topics of discussion centred on Fernandez, who has been the source of so much speculation that Real Madrid released a statement on the rumours.

Real are known to be among his admirers, though the La Liga giants managed by Jose Mourinho insisted they are not in talks for Fernandez, who is valued at £120million by Chelsea.

‘Yes, we have spoken,’ Alonso said when asked about the Argentina international who is set to face England at the World Cup this Wednesday. ’As you can understand, it remains private, but we have spoken.’ When pressed on whether he wants to keep Fernandez, Alonso said: ‘Yes.’

Chelsea are getting to work in the transfer window, having sold Marc Cucurella to Real for £47.5m, Tyrique George to Everton for £22m, and Andrey Santos to Manchester United for £50m. Santos’ switch was confirmed on Monday, shortly before Alonso’s unveiling.

‘We need to make important decisions, right decisions,’ Alonso said. ‘We have a strong base already built. Now we have to build and build this mentality, to be competitive on the pitch, to win games and enjoy it. We are ambitious. It is important we build the right mentality to compete. I am optimistic to think we will have a great season.’

Cole Palmer has returned to pre-season training, which started on Thursday, after being excluded from Thomas Tuchel’s England squad for this World Cup.

Alonso said the 24-year-old Englishman has returned in the ‘mood’ for a ‘great season’.

‘We have had a few training sessions already,’ Alonso said on Palmer. ‘From the first day, you can see he's a special talent, a special player. It's not easy to have one of those. You can notice his quality, how he's able to play, the right decision in the right spot.

‘So I'm happy that he has come in a good mood, a good mindset to have a great season, and we are really looking forward to getting the best from him.

‘If we are able to build a strong team with the proper stability to find the key players, for sure, Cole is going to be one of those key players in the attacking part.’

As reported by Daily Mail Sport, Alejandro Garnacho has not returned for pre-season because he is for sale after a single season. Alonso also confirmed: ‘The situation is we've spoken with the sporting directors. There's interest in him from other clubs. It hopefully finishes in the best way for all parties.’ Garnacho was signed from Manchester United for £40m last summer.

Alonso was unwilling to reveal whether he will be prioritising a back three or a back four, with the new Chelsea boss saying: ‘For sure I have something in mind. This is my job. We want to be active, brave, play good football, compete well, but above that, we need good mentality.

‘That’s fundamental to understand what to do and what it takes in each moment. We want to show that we are ready to go. Once we are closer to the start of the season, we will reassure that with all the players.’