The Brazilian joined Chelsea from Brighton in 2025 and scored 20 goals, providing nine assists in 50 appearances to win the club's Player of the Season award for 2025-26.
Pedro has continued his impressive form under coach Xabi Alonso, forming a dangerous attacking trio with Palmer and Morgan Rogers.
Speaking to ESPN, the 25-year-old explained how Palmer helped him settle into life at Stamford Bridge.
"I told him I was coming to help, that I didn't want to take his spot - nothing like that," Pedro said.
"And that's where a friendship was born that we carry on both on and off the field."
Pedro believes Chelsea's welcoming dressing-room atmosphere has played a major role in his development as a centre-forward, with players such as Reece James and Moises Caicedo also helping him adapt.
The Brazilian has made an excellent start to the current campaign, scoring five goals and providing three assists in six Premier League appearances.
"At Chelsea I feel very comfortable," he said. "It's a different season, with a coach who gives me a lot of confidence, and I think that's a big part of my performance so far this season."
Alonso's preferred 3-4-2-1 formation has allowed Pedro to benefit from the creativity of Palmer and Rogers, who operate behind him in attack.
"I think it does make it easier," Pedro said. "I have Cole and Morgan there to help me, to feed me the passes - you can see that the start of the season has been really good."
Despite his club form, Pedro was left out of Brazil's squad for the 2026 World Cup by coach Carlo Ancelotti.
His progress in England began at Watford, where he played from 2020 to 2023 before moving to Brighton and eventually Chelsea.
Pedro considers his decision to stay at Watford after their relegation to the Championship in 2022 a defining moment in his career.
"I worked hard and proved that I could overcome that challenge," he said. "That's the moment when I said to myself: 'No, I came here, and I'm going to succeed here.'"
The forward also revealed the personal philosophy that has helped him overcome setbacks.
"I have a phrase tattooed on me that says: 'Just as there are bad moments, there will be happy ones too.' I try not to focus on the past... what's done is done."
Chelsea, who sit fourth in the Premier League, will aim to maintain their strong start when they host Tottenham Hotspur at Stamford Bridge on Saturday.
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