I'm with Whitty on this one:

The sound of "It will rain, most likely" is ok to my ear; also, "It will most likely rain" sounds ok, too.

But "It will likely rain" sounds weird. I don't know that I've ever heard that construction.

"It is liable to rain" sounds old-fashioned.

Then there's my grandma Etta's, "I kin see black clouds in the element! Likely to rain today!" She's the only person I know who refers to the sky as the element.

Best regards,
WeatherWind