Can't we say " Look at those dark clouds.It is likely/bound/due to rain " ?
Let us look at all those options mentioned in your question. And we will see what comes first in my mind.
Look at those dark clouds. It is likely to rain = It ought to rain today. It might be raining after some time.
Look at those dark clouds. It is bound to rain - It is quite certain that it'll rain (It is close to 'likely' but a bit more in degree of certainty). OALD's example: It's bound to be sunny again tomorrow.
Look at those dark clouds. It is due to rain = The existence of those dark clouds is because of rain!
So, in the context defined, likely or bound work.
Maulik and tunny are correct about their interpretations of "It is likely to rain", "It is bound to rain", and "It is due to rain."
Another option is "We're due for rain." In this usage, rain is assumed to come more-or-less on a schedule. Either it is now a time at which "we" expect rain, or the rain is "overdue". Furthermore, "we" are under the influence of a "gambler's fallacy" -- "we" assume that if the rain is "overdue", then rain is especially likely to happen soon.
There are several common situations where an American might say "We're due for rain."
There has been a drought. For example, "we" are in what is historically a wet season, but "we" have gone an unusual length of time without rain.
The dry season historically ends soon, and "we" are expecting the wet season to start soon.
A weather forecast (or an almanac) predicts rain soon (or in the recent past).
Some places (during certain seasons) have rain at predictable times of day. For example, many places have a brief thunderstorm in the middle of most summer afternoons. Other places often have misty mornings.