Asensio has been in red-hot form for Real Madrid at the start of the 2017-18 campaign, which earned him a spot in the latest Spain squad for the 2018 World Cup qualifiers against Italy and Liechtenstein.
"Asensio? The fact that he's here speaks for itself. His performances don't come as a surprise and that's important for a team like Real Madrid because we followed him and knew about him already," Iniesta told reporters.
"It's good news for Spanish football. I hope he's helped and taken care of, so we can enjoy him in the national team for many years."
Asensio scored 10 times in 38 appearances for Real Madrid last season, and has already netted four times in five matches for the Spanish champions at the start of the new campaign.