There's possibly some filling-in-the-gaps thing going on here by journalists in Australia, but several sources from that part of the world are reporting that Cesc Fàbregas will miss Chelsea's post-season tour that has matches scheduled in Bangkok (May 30) and Sydney (June 2). They are basing this on Vicente Del Bosque's words about the Chelsea midfielder when announcing the Spain squad yesterday.
"We had a problem with Cesc, who is going to have an operation on his nose. We have included him like [Sergio] Ramos because they have guaranteed us they will be ready for June 1."
-Vicente Del Bosque; source: Fox Sports
Assuming Del Bosque has his pronouns in order, we can take this to mean that Fàbregas will have surgery prior to the international games, rather than after. I haven't seen any official word on this from Chelsea, but we're notoriously bad at reporting injuries and such (such as Mikel's surgery earlier this season, or the status of Diego Costa's hamstrings, or the full extent of Oscar's head injury, etc). Also, I was under the impression that Cesc already had one procedure done on the nose when he was originally fitted for his mask, but perhaps that was more of a temporary fix.
In any case, with the squad due to fly out today, we'll know soon enough who's on the plane and who's off to take care of other business.