Alonso, currently 43, is widely expected to succeed Carlo Ancelotti following Madrid's final game of the season against Real Sociedad.
While the club have not officially confirmed the appointment, Alonso is tipped to take charge ahead of next month's FIFA Club World Cup.
"It looks like Xabi is going to be the one coming in even though it's not official," Carvajal told reporters.
"Only time will tell if Xabi is the right man to turn this year around, as we haven't won any of the three major titles. But that's football. In the end, results are what determine the future of coaches, players."
The former Real Madrid midfielder is leaving Bayer Leverkusen after a highly successful spell. In nearly three seasons at the German club, Alonso guided Leverkusen to a historic undefeated Bundesliga campaign and a domestic double in 2023-24.
"Xabi has just had two fantastic seasons with Bayer Leverkusen and I think he will do very well," added Carvajal.
"He knows the club better than anyone, he's been a player, he's defended the badge for many years, he knows what it means to be a Madrid player, and I think that's also a plus for him as a coach."
His return to Madrid comes in the wake of a turbulent season. The club were eliminated in the Champions League quarterfinals by Arsenal, lost the Copa del Rey final to Barcelona, and suffered a crushing 5-4 defeat to Barca in El Clásico on 11 May - a result that ended their title hopes. Madrid will finish second in La Liga behind their arch-rivals.
Carlo Ancelotti, who has won 15 trophies across two spells in charge, including a Champions League and LaLiga double in 2022-23, is set to become Brazil's national team manager.
Arsenal are reportedly gearing up for a transformative summer transfer window, with Mikel Arteta and new sporting director Andrea Berta driving an ambitious recruitment push to end the Gunners' five-year trophy drought.
Chelsea are reportedly preparing a surprise summer bid for Brazilian winger Rodrygo as the player's future at Real Madrid grows increasingly uncertain.
Arsenal are ready to shake up the transfer market by offering star defender William Saliba to Real Madrid in a daring bid to secure winger Rodrygo, sources have revealed.
Kylian Mbappe heads into Real Madrid's final La Liga match against Real Sociedad on Saturday with more than just Carlo Ancelotti's departure on his mind.
