French Montana's Going West Side ... of Manhattan

French Montana's ready to drop major cheddar on a new pad really close to his hometown, but far, far away in terms of real estate prices.

Sources tell us the Bronx-raised rapper went shopping earlier this week as a first-time buyer on Manhattan's West Side. We're told John Lecce, of Batra Real Estate Group, showed him luxury high-rise condos in the $5-10 million range.

French is considering cribs in the SoHo, Tribeca and West Village neighborhoods.

Looks like he'll be bicoastal, since he just bought Selena Gomez's old mansion for a little more than $3 mil.

As far as when he'll pull the trigger in NYC, we're told he's in no rush and willing to wait for the right location ... location, location.