It's not correct.
According to the Cambridge Grammar of the English Language, single-syllable adjectives typically take "-er" and "-est" forms (eg "small → smaller → smallest") while multi-syllable adjectives typically use "more" and "most" (eg., "beautiful → more beautiful → most beautiful"). There are of course exceptions to this ("fun" springs to mind) but words tend to be used one way or the other, andso with "cheapest" isbeing the idiomatic choice that makes "most cheap" incorrect for the context you refer to.
Note thatThat said, 'cheap' has other meanings beyond monetary cost and can imply low quality or worth (eg "that was a cheap shot"). Also, 'most' is sometimes used as an intensifier rather than denoting a superlative (eg "that was a most pleasant afternoon"). In those contexts, it might not be so unusual to say something was "most cheap" but it's a bit convoluted.