The Belgium international has recently celebrated 10 years at the Etihad Stadium but is out of contract in the summer, with talks over a new deal having yet to begin.
Despite the raft of options available to Guardiola, Kompany has already made five appearances this term and remains a key part of his plans.
And the Spanish coach wants to keep the skipper for another year and has hailed his impact on the younger members of his squad.
"Yes, that is my wish," Guardiola told the media when asked about whether he wanted to keep Kompany. "Ten years is a lot. It's incredible.
"He played the Carabao Cup like it's the final of the Champions League.
"That means a lot to me.
"If he plays five minutes then they are going to be the best five minutes in his life.
"He is a good example for Phil Foden and the rest of our squad.
"Unfortunately in the past it was the injuries, but I think in the last few months he's feeling better."
Kevin de Bruyne, David Silva, Fernandinho, Gabriel Jesus and Ederson have all agreed new contracts in the last 12 months.
Despite failing to agree an extension in the summer, Raheem Sterling is the next in line for a new deal and after three goals and two assists this season Guardiola can already see an improvement on last term.
"I think his performances are higher," he said. "My feeling is that he's more mature than last season. I like it.
"Sometimes it's about the statistics but also how he produces it.
"Maybe I'm wrong but my feeling is that he believes in himself more, he is taking on more responsibility. That's good.
"Maybe the stats are wrong. But our target is to make them feel better than the previous season."
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