Our Kardashian sources tell us ... Tristan Thompson's plan to simply rent a place in L.A. went out the window as soon as the couple found out she was pregnant. Now we're told he's looking to buy a pad in Bel Air, Bev Hills or the Hollywood Hills.

As we reported ... Khloe and Tristan were out hunting for a rental for him in July, looking for places in the $60k a month range. Our sources say now that he's planning to become an L.A. homeowner ... his budget's around $20 million.

We're told Tristan wants his own place in the city so they don't have to drive back to Khloe's house in Calabasas ... which is about an hour away.

And he probably wants to design his own baby room, too.