Mansun

I think Sauron gave away the idea that he did have a decent understanding (so he thought!) with Saruman. If you remember, Pippin had an encounter with Sauron through the seeing stone, in which Sauron thought he was for a moment communicating with Saruman, asking " Why have you neglected to report for so long?". This implies that Saruman actually betrayed Sauron, but it is highly likely that should Sauron retain the Ring he would brush aside even a loyal Saruman to some low key mischief job, assuming that the Mouth of Sauron was to become the lieutenant of Isengard.

The fact that the Mouth of Sauron also made out that the Darklord no longer trusted Saruman to be worthy of that role when all was to be won at the black gate suggests that he did most likely work well with Saruman initially, but then was betrayed by him. Sauron must have thought Saruman was incapable of getting the Ring in the first place, and even if he got it, Sauron would know exactly where it was, and would bend his power towards Isengard like a storm (or quicker).