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The relative merits of the two sports are up for debate as Ultimate Fighting Championship superstar b prepares to make his boxing debut against Floyd Mayweather in Las Vegas on Saturday.
McGregor's total lack of boxing experience has proved a bone of contention for many in the build-up to the fight, but Joshua said he would enjoy taking on an MMA fighter, albeit with conditions.
"I like fighting. I'd do whatever," the IBF and WBA heavyweight champion told Britain's Press Association in comments published on Monday.
"I'd probably get beaten. The only thing that they can't do is submissions, but they can kick, elbow, bite -- whatever they want. Just no submissions.
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"I can't beat a guy (via submission). That takes a lot of time to learn the skills and submissions, which I don't have the time for.
"But when it comes to pure aggression and fighting rules, I can definitely fight, so I don't mind that.
"It wouldn't be a problem. If you look at most boxers who've crossed over to MMA, they get beaten on the ground.
"James Toney, Roy Jones, they were phenomenal boxers, but they just couldn't compete in the cage because of the 'ground and pound' game."
Joshua, who will not be ringside on Saturday, believes Mayweather will "probably" win by a "landslide".
Joshua, 27, is awaiting confirmation of his next title defence against Bulgarian Kubrat Pulev, which is expected to take place either in Las Vegas in November or in Cardiff in October.