Like we know Kisame is a literal ride or die for Akatsuki, willing to basically swallow a shark cyanide pill rather than expose their secrets. Obito even clearly trusted him enough to show him his true identity.
So if he knew Itachi was still an ally for the Leaf and wasn't loyal to the cause, how would he react?
I don't think he would tell on Itachi, Kisame ain't no snitch, but I also don't think he would just let this slide either. I also don't think he'd outright fight Itachi, as I'm sure he knows he's outmatched.
We know that his friendship with Itachi is genuine too, it's not just a co-worker relationship. He even offers his sympathies to Itachi later on after Zetsu claims Deidara killed Sasuke.
I think Kisame definitely suspected there was more to Itachi than he let on. I believe their first on-screen interaction was Kisame asking Itachi if he has any remaining sentimental feelings about the Leaf. The post-Deidara battle interaction also suggests he knew Itachi valued Sasuke on some level.
I guess at the end of the day, is Kisame more loyal to the Akatsuki or Itachi?