One approach is mentioned in The Challenge of Creation, by R' Natan Slifkin, in footnote 2 on page 277:
... others explained that the deluge did not cover the entire earth, hence not every species of animal had to be taken on board; see Rabbi Dovid Tzvi Hoffman, commentary to Genesis, pp. 140-141; Rabbi Azriel Leib Rakovsky (disciple of Rav Yaakov Karliner, author of the Miskenos Yaakov), Shelemah Mishnaso to Berachos 56b, and Rabbi Gedalyah Nadel, BeToraso Shel Rabbi Gedalyah pp. 116-119. For further discussion of various approaches to the topic of the deluge, see Rabbi J. Hertz's "Additional Notes to Genesis" at the back of The Pentateuch.
Here's my translation of the particularly relevant part of BeToraso Shel Rabbi Gedalyah, from page 118, which can be found on page 65 of the PDF linked on the sidebar of this page (paragraph breaks and links mine):
"To destroy all flesh ... which is under the heaven, all that's on the land will perish" - We've already said that "which is under the heaven" refers to the heaven over this land, the land east of Eden. To a person living in this area, this is the whole world, everything that he can see and relate to.
One can bring evidence from a Gemara for this. In Bechorot (55a), we learned, "One who vows oneself off of the waters of the Euphrates is forbidden from all the waters in the world," because the sources of the Euphrates are high, and all the waters in the area go up and flow from them, due to the capillary action of liquids. Are there no places in the whole world higher than the origins of the Euphrates, that don't draw at all from the Euphrates? - Of course, there are, and the meaning of the phrase "all the waters of the world" clearly is: in the whole area, in the whole Middle East. That's "the whole world" to someone living in this area.
And we also learned in Zevachim (113a) that R' Yochanan and Reish Lakish disagreed about whether the Deluge descended upon the Land of Israel as well or not. Is the Land of Israel not "under the heaven"? We see that it's possible to think that the waters of the Deluge didn't cover the entire world. And one can understand that they disagreed with respect to the Land of Israel, since it's near Babel, if it was also afflicted as part of the area that the Deluge descended upon, or if - due to its holiness or some other reason - a land which "is not rained upon on the day of rage."