Having moved from Atletico Madrid in a club-record €70 million (£63m/$79m) deal, 23-year-old Rodri made his first appearance in a City shirt in Wednesday's Premier League Asia Trophy clash.
The Premier League champions had little trouble in dispatching West Ham 4-1 in Nanjing, with Raheem Sterling netting twice off the bench following goals from David Silva and Lukas Nmecha in the first half.
Rodri looked comfortable in the middle of the pitch despite being tasked with marking the lively Michail Antonio, and after the game Guardiola shared his thoughts on his young compatriot.
"He is a young, typical defensive midfielder who thinks very quickly. I hope he is here for a long time," Pep explained to reporters.
"Rodrigo is tall, which for a short side like ours is very good. He is great at set-pieces but we didn't buy him for that."
The Spain international's signing is part of a regeneration process going on behind the scenes at the Etihad Stadium focusing on the signing of future stars.
Indeed, of the three new faces brought in so far this summer Zack Steffen, who was immediately released on loan to Fortuna Dussledorf following his arrival from Columbus Crew, is the eldest at 24.
Pep hopes to continue that youth-oriented recruitment policy and also sees great things in his new midfield lynchpin.
"Ever since we arrived here we have tried to buy players who are 21, 22 or 23 years old," he added.
"[Rodri] is a Spain national team player and there they call him 'the next Busquets'. I think he is a very good player."
Rodri played a single season with Atletico after moving from Villarreal in 2018, and missed just four of his team's Liga fixtures as they grabbed second place behind Barcelona.