The Spaniard faced the media for the first time ahead of pre-season after being appointed Chelsea head coach at the end of last season.
Palmer, Joao Pedro and Levi Colwill were among the senior players to report back for training this week, alongside new signings Geovany Quenda, Emmanuel Emegha and Dastan Satpaev, as Alonso began work with his new squad.
Alonso eager to make mark
Asked what attracted him to the Chelsea job, Alonso spoke of the club's potential and his ambition to build a winning team.
"The excitement is the club, the squad and the opportunity the owners have given me to come to this great club," he said. "We want to excite the supporters, win games and be successful.
"I want to enjoy it. I want to be part of this club and work closely with the board, the players and all the staff.
"I see a club with enormous potential. We will have to make important decisions — the right decisions — but I think there is already a strong foundation in place.
"Now we have to build on that, develop a winning mentality, be competitive on the pitch, win matches and enjoy the process."
Alonso wants Fernandez stay
Alonso was also asked about the futures of several players, including Enzo Fernandez, who has been linked with Real Madrid, and Alejandro Garnacho, who has been the subject of transfer speculation.
On Fernandez, Alonso confirmed he had spoken to the midfielder but declined to reveal the details.
"We have spoken, but that remains private."
When asked directly whether he wanted Fernandez to stay at Chelsea, Alonso replied simply: "Yes."
Discussing Garnacho, he added: "We've spoken with the sporting directors. There is interest in him from other clubs, so we'll see how the situation develops. Hopefully it ends in the best possible way for everyone."
Palmer praised after first training sessions
Alonso also spoke warmly about Palmer after working with the England international for the first time, describing him as a special talent who will play a pivotal role this season.
"We've had a few training sessions already and, from the first day, you can see he's a special talent," Alonso said.
"Players like him are not easy to find. You notice his quality immediately, the way he wants to play and the decisions he makes.
"I'm pleased he's come back in a good mood and with the right mindset to have a great season. We're looking forward to getting the best out of him. He will be a key player."