Palmer, after being left out of England's World Cup squad will be reflecting on a dire campaign filled with injuries and a severe lack of goal contributions in a Chelsea side who missed out on Europe.
The 24-year-old is being linked with a move to rivals Manchester United as he considers his future ahead of the summer transfer window where he may be thinking of leaving for European football.
Speaking with Stake, Evra revealed that he thinks Palmer could get back to his old self under Alonso who will begin his role on July 1, 2026.
“Let’s not forget, Palmer has been injured a lot. Palmer doesn't need any manager to get him back to his best. Injuries are not easy to recover from.
“Sometimes, some players get injured and they get one or two years to get back to their level. But knowing Alonso and him accepting the job, I wouldn't be surprised if Palmer is shining again at Chelsea.
“As a Frenchman, I would be happy if Cole Palmer doesn't go to the World Cup. England will be less dangerous. He has to take care of himself.
“I played more than 900 professional games. And if you ask me, how many games I played where I was 100% fit. I will tell you maybe five or six games, because you always have a knock. You always hear Thierry Henry say the same and it's the truth. And people don't know because in training, you can receive a knock.
“For Palmer and his family, of course, it's beautiful. They go to the World Cup. But if you really need to do that surgery and go back to his best, yeah, it will be better for him to stay home.”
Alonso, with no European football at all to force him into rotation, will have a lot more flexibility with the side which could benefit Palmer who will want to see the club win trophies this season to halt further transfer talks.