England manager Thomas Tuchel said in September that Palmer had missed "too many opportunities" to play for the national team after he pulled out of the squad with an injury.
The German repeated that message after naming his latest squad on Friday for Nations League matches against Croatia and Spain.
Palmer, 24, who was omitted from Tuchel's World Cup squad, has had an inconsistent start to the season at Stamford Bridge.
He has scored five goals and provided three assists in 11 appearances in all competitions, forming a potent front three alongside Morgan Rogers and Joao Pedro.
But he was sent off in a 2-0 defeat to Tottenham last month and has not scored from open play in the Premier League since August.
"I'm very happy with his quality, attitude and the impact he's having on the rest of the team," said Alonso.
"We speak about Chelsea, we have enough on our plate. We have to focus each weekend and that's what I can impact and talk about."
Palmer has made just five appearances for England since scoring in the Euro 2024 final, a 2-1 defeat to Spain.
"He needs to focus on playing good football and enjoy playing with Chelsea," said Alonso.
"We spoke about the red card after the Spurs game, but most of the things apart from that are about the game, football and what we can do better."
Chelsea, fourth in the Premier League, could be boosted by the return of number one goalkeeper Emi Martinez for Sunday's trip to struggling Sunderland.
Martinez suffered a fractured jaw just three weeks ago, but the Argentine international has been cleared to play in a face mask.
"It (the face mask) is not the most comfortable thing," said Alonso. "He's been training almost the whole week with it and for a certain period of time he'll have to deal with it."