Palmer, left out of England's World Cup squad this year after a persistent groin injury affected his form, was called up by Thomas Tuchel for Nations League fixtures against Spain, the Czech Republic and Croatia.
However, Palmer was forced to pull out of the squad due to a recurrence of the issue, with Tuchel saying the 24-year-old "misses too many opportunities" to play in an England shirt.
Asked about Tuchel's comments on Friday, Alonso told reporters: "The most important thing for Cole is to be fully fit, that he enjoys his game, that he is feeling OK.
"Whenever he is not, like in the Brentford game, we could see that he was struggling. He's committed but he needs to be fully fit to play. We need him - the club and the national team," the Spaniard added.
He was speaking ahead of a Premier League meeting with Bournemouth.
"Now he's fine. He's been feeling better this week. We use the first two weeks for him to recover. It's a little bit from the pubalgia (groin injury) he had."
Chelsea, 10th in the Premier League standings, host 17th-placed Bournemouth later on Saturday.