I would guess Saruman, like Sauron, expected the Ring to be used as a weapon to destroy the Dark Lord.
Of course, as he knew Gandalf and Elrond personally, he might have known better - but it seems highly unlikely.
Up to the breaking of the Fellowship on Amon Hen (where Saruman lost track of the Ringbearer) - the Fellowship followed the road to Minas Tirith, so Saruman could guess wrong and still trace their route for a long way.
And my supposition that Saruman did not know is shared by Gandalf, as he explained Saruman's doubts in The White Rider. Of course Gandalf could have been wrong, but I see no reason to suppose so in this case; in fact, a major theme of the book is that the forces of Evil could never guess the Ring would be actually refused, and if Saruman guessed that it would ruin the whole story.