Mbappe, who matched Cristiano Ronaldo's club record of 59 goals in a calendar year during Real's 2-0 LaLiga win over Sevilla last month, is nursing a knee injury.
The France forward, who has scored 12 goals in nine matches against Barcelona, flew to Saudi Arabia on Friday to join the squad ahead of the El Clasico showdown in Jeddah.
"He's much better," Alonso told reporters. "Against Atletico, he was just about ready, and we decided not to rush him, but we kept in mind that he might be able to play in the final.
"He flew yesterday and will train with the team today. We'll assess him and decide whether he'll start or play a little less. It's a decision we'll make with the player, the coaches and the doctors. The moment we're in and what's at stake ... It's a controlled risk."
Real beat Barcelona 2-1 at the Bernabeu in October after losing the Spanish Super Cup final and the Copa del Rey final to their arch-rivals last season.
"We're focused on what we have to do and how to play the match," Alonso said. "It will be a match with moments for everything. We have to have the necessary energy."