Romney said "in all likelihood" he would win the 1,144 delegates needed to get the GOP nomination, the Los Angeles Times reported.
"We have had 35 contests in states, and of course the islands, and it's kind of hard for anybody to get the delegates to pass me at this stage, so it looks pretty good," Romney told Fox News Monday.
"But you know, the other guys are still in there so we're going to keep on campaigning in each of the early primary states until we have the nomination wrapped up."
Romney also welcomed fellow candidate Newt Gingrich's pledge to support him once he wraps up the nomination.
Gingrich said Sunday he believes it's clear Romney is most likely to be the nominee and he had "done a very good job of building a very substantial machine" capable of defeating Obama.