Facing 19 Fingers and One Big Eye

[Inziladun]

I believe by that time Sauron likely already had all the useful information that Saruman could offer, courtesy of their conversations by Palantír. I don't think Saruman knew of the plan to destroy the Ring, as either Sauron would have gleaned that from Saruman's mind during one of their conferences, or Saruman would have willingly informed Sauron so as to receive his favour in victory. If Saruman himself could not lay hands upon the Ring, that had to have been his "Plan B".
Sauron was well aware of Saruman's doings and did not need him, though I'm sure repaying Saruman for trying to get the Ring for himself would have been a priority for Sauron once the West was beaten.