Lindsay Lohan and Woody Allen -- The Manhattan Dinner Mystery

Look out Scarlett Johansson ... Woody Allen has a new buxom, young muse in his sights ... and that muse is Lindsay Lohan.

The unlikely duo was spotted out in NYC last night at fancy-schmancy Philippe restaurant -- and we're told this isn't their first spin on the friendship bicycle.

Sources close to Lindsay tell TMZ ... Allen and Lilo have been friends for years now and he's one of her biggest supporters -- never jumping on the judgment bandwagon.

We're told there are no projects officially on the books right now, BUT sources tell us they've been throwing around the idea of Lindsay being in one of Allen's future films -- which would be huge for Lilo, since his last flick, "Midnight in Paris," was nominated for a bunch of Academy Awards.

We're also told Lindsay has nothing but respect for the quadruple Oscar-winning director and would LOVE to work with him.