The fellow Spaniard believes the former Atletico Madrid man, who put pen to paper on an initial loan deal during the final minutes of transfer deadline day, will eventually be a “very good” player for the Blues.
Saul was hooked by manager Thomas Tuchel at half-time on his Chelsea debut, appearing just once since and watching five games from the bench.
But Alonso is backing the 26-year-old to prove himself following his “adaption phase.”
“He’s a newcomer,” he told Cadena SER when asked about Saul’s start to life on the pitch in West London.
“He’s in the adaptation phase, but he’s a great player and he’s going to be very good for us.”
The left-back was also quizzed on Tuchel’s instantaneous impact at the Bridge, leading the Blues to winning the Champions League and finishing inside the Premier League top four last season, despite only taking over from Frank Lampard in February.
“With us, he was able to change the team very quickly and now he wants to continue improving us,” Alonso explained.
“We are very pleased with the coach since day one, and to have him around this season.”
He went on to say: “I’ve had a lot of great coaches. At the end of the day everyone has their things.
“It is clear that he is a great coach, in the footballing and the personal aspects.
“He reads matches really well, we prepare really well under him. It is an advantage having a coach like that.”
Alonso played 90 minutes in the 2-1 victory over Italy, booking La Roja’s place in Sunday’s showpiece against France in Turin.
Having made just one appearance for Real Madrid in his youth, the ex- Fiorentina defender has spent the vast majority of his career in England – including spells with Bolton Wanderers and Sunderland – and is now in his sixth season at Stamford Bridge.
Understandably, he harbours the ambition of playing in his native La Liga before he hangs up his boots.
“I am doing very well [at Chelsea] and also, before retiring, I would like the opportunity to play in La Liga,” Alonso added.
“It is not something urgent, I am doing very well at a great club and fighting for big titles. I have two years in my contract and we will see what happens in the future.”