George Martin wanted to release "Yesterday" as a Paul McCartney solo single. He knew McCartney had written it on his own, and he saw him record it without any contributions from any of the other Beatles. A similar thing happened with the Beach Boys, when "Caroline, No" would be released as a Brian Wilson solo single and reach Number 32 on the charts in March of 1966. But when Pet Sounds came out on May 16, "Caroline, No" was in the mix as just another Beach Boys track.
But that was all in the future in June of 1965, when McCartney cut his song. It's not clear whether Martin broached the subject with Paul, but he did mention a solo release to Brian Epstein. But Esptein had a clear opinion on the issue: It wasn't going to happen. He told Martin, "No, whatever we do we are not splitting up the Beatles."
Sixteen months later, John met Yoko.