Real Madrid's Alonso unsure of Mbappe absence length
The French striker was diagnosed with a knee strain on Wednesday, expected to keep him out for at least three weeks.
"We'll try to make it happen quickly, it depends a lot on how he feels, but we'll try to get him back as quickly as possible," Alonso told a news conference.
"When is as soon as possible? That's the question. I don't know."
The coach said he hopes Mbappe will be back to take part in the Spanish Super Cup, with Los Blancos facing rivals Atletico Madrid in the semi-final on January 8.
Mbappe, 27, is Madrid's top goalscorer with 29 goals this season across all competitions in 24 appearances.
Alonso will be without the striker for Sunday's La Liga clash against Real Betis at the Santiago Bernabeu.
Madrid trail leaders Barcelona by four points, with the Catalans visiting city rivals Espanyol on Saturday.
Alonso came under heavy pressure in December amid Madrid's inconsistent form, with his future still on the line in the weeks ahead.
One bright spot was Brazilian forward Rodrygo Goes bursting into form towards the end of 2025, and Alonso wants him to continue in the same vein.
"He played some very good games at the end of the year... we need him, like everyone else," said Alonso.
"To make up for Kylian's absence we have different options, and Rodrygo is one of them."