Aguirre's position as Atletico coach has been the source of much debate in recent times, and the Mexican was still quizzed about the situation following Sunday's 1-0 win over Deportivo La Coruna which guaranteed the Madrid side will be playing Champions League football for the first time in 11 years next season.
Ensuring a place in Europe also triggered a clause in Aguirre's contract that automatically extended his deal until 2009, and Maxi told Spanish newspaper Marca: "Aguirre has to continue."
He added: "I'm really happy about what has been achieved after so many years. Now we have to get through the qualifying round and enjoy this moment with the group and with the people at the club.
"Everybody's dream is to play in a competition as beautiful as the Champions League."
Argentina international Maxi also backed his compatriot Sergio Aguero to stay on at the club in spite of rumours linking him with a summer transfer.
The 19-year-old has attracted a huge amount of reported interest from other clubs this season after notching 26 goals already, but has also reiterated his desire to stay.
"I think that Aguero is going to stay, although he has a lot of quality and he won't be wanting for offers," Maxi said.
"I hope Atletico Madrid can keep hold of him for as long as possible.
"He's happy at the club, in this city, and I hope he stays for many years to come."