I highly doubt it. Then again, the former congressman never explicitly ruled it out (via The Blaze):
I don’t think West will for the very same reasons he himself raised during the segment above: First, if -- if --he were to challenge Marco Rubio from the Right in 2016, his chances of winning are decidedly slim. This is obvious. Rubio, after all, is a sitting United States Senator who is incredibly popular in Republican circles -- despite his unwavering support for “comprehensive immigration reform.” In short, West would need to raise a ton of money to even have a chance. And, as he himself notes, that’s “a pretty heavy lift.”
Second, the media would love the theatrics of a Tea Party Republican challenging … a fellow Tea Party Republican. Question: How on earth would a sensationalized, brutal primary between two national Republican figures help unite the party? The media would have a field day, to put it mildly, and it would be a complete and total PR disaster. Of course, Rubio’s decision to stand with Schumer et al vis-à-vis immigration reform is certainly disheartening, but does the guy really deserve to be primaried for it? I sincerely hope most reasonable people would at least agree on this: the former congressman's talents and political experience could be put to much better use than ousting Rubio from elected office. Which is exactly why I don't believe, when push comes to shove, he'll actually go through with it.