I think the reporters at House of Saud mentioned that Oman had been consulted by Iran near the start of the conflict, and Iran’s stated goal is Oman and Iran together control shipping through the strait.

Equally though, Oman has been pretty content to sit back and not draw the ire of either side which is sensible enough too. Besides, for a smaller Middle Eastern nation it’s not as if its government openly supporting either side would win it much favour.