The 26-year-old arrived from Fiorentina in 2016 and had an immediate impact as he helped his side win the Premier League title.
Speaking to Cadena Ser (h/t Sean Kearns of Metro), Alonso said he would like to play in his homeland but has no immediate plans to leave Stamford Bridge, saying:
"I'm very happy at Chelsea but I would like to return to Spain one day.
"Before I retire I'd like to play in La Liga. I haven't played much there.
"But i'm very happy in London. All I think about is the game against Crystal Palace."
Alonso's performances were one of the biggest surprises under coach Antonio Conte last season, and the former Bolton Wanderers player has proved himself to be one of the best in his position in Europe.
The full-back featured in 31 Premier League appearances last term, according to Squawka, scoring six goals and creating 23 chances.
Alonso's statement will please Chelsea fans, and the Spaniard appears set to remain with the champions for the foreseeable future.
In other Blues news, Juventus defender Alex Sandro remains a target for Conte, despite Chelsea's failure to grab the player last summer.
Il Corriere dello Sport (h/t Luke Gardener of the Daily Star) reported the Brazil international is on the brink of signing a two-year contract extension with the Old Lady, but Chelsea will try one last time to capture his services in January. Chelsea reportedly had an offer of £53.75 million rejected for Sandro, but Conte will submit one final bid.
The player featured in 38 matches in Serie A and the UEFA Champions League last season, per WhoScored.com, as Juve once again stormed to the Italian title.
Sandro has been impressive for his club, but with Alonso first choice at the Bridge, it is questionable whether Chelsea need to pay a huge fee for a left-back.
Sandro is the same age as Alonso, so it would make more sense if the Blues targeted a talented young player with a cheaper fee and wages, able to deputise for the impressive Spanish full-back.