The couple has enjoyed a low-key relationship, with British-born Watts only recently breaking her silence on the romance.
And while representatives for the screen stars have yet to comment, pals say Schreiber has already proposed.
A source says, "Naomi not only said yes, but she wants to get married as soon, and as secretly, as possible.
"Liev doesn't want to waste any time. He is absolutely thrilled Naomi is going to marry him. He says it's something he's been wishing for almost since their first date. And he's already told her that he wants to have lots of babies. Right away!"
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