Azpilicueta has spent ten years at Chelsea after joining from Marseille in the summer of 2012 and has won every available club honour with the Blues in his time in West London.
Azpilicueta's contract expired this summer but Chelsea exercised their option to extend it by a further year.
Having swooped to take Andreas Christensen away to the Camp Nou already this summer, Barcelona are looking to poach the experienced Azpilicueta too from Stamford Bridge.
Tuchel is however not prepared to lose his captain despite the latter's desire to return to Spain.
"It's a tough question because I'm not sure if I want to give Azpi what he wants," said Tuchel, as quoted by Standard Sport.
"At some point it is about what we want. I just made the comparison about how much we fought for [Kalidou] Koulibaly, who is a national team player and roughly the same age.
"He is a hugely important player for Napoli but we have a Spanish international who is the captain at Chelsea. I see him maybe at the same level, but Barcelona don't see him on that level. So I am not sure if I want to give him what he wants as he is a huge player.
"We don't think so much about other clubs. The focus is on us and what we need. I said that to him and I say it to you that I understand on a personal and a career level. But I am not only in this role to give him what he wants. I am a manager for Chelsea who wants to do what's best for Chelsea.
"He doesn't like it but he understands. It is tough for him because the other club is permanently on him. On September 1 when things calm down, then he can play on his highest level."
