The idea that I've outsold Robert Heinlein and Frank Herbert just broke my brain. (Also I don’t believe it.) http://thewertzone.blogspot.co.uk/2015/03/the-updated-sff-all-time-sales-list.html/a>— Neil Gaiman (@neilhimself) March 14, 2015
The page he links to puts him at #17 for all time, with 40+ million sales; Heinlein at #26, with 30+ million; and Herbert at #30 with a rather precise 26 million.
I have checked the figures with my favourite stats sites, Goodreads and LibaryThing, which of course provide information only about their users. But the evidence from them is that, if anything, the article underestimates Neil Gaiman's lead over the other two.
On Goodreads, users have logged 694,192 individual books by Frank Herbert, 702,287 by Robert A. Heinlein and 2,847,588 by Neil Gaiman.
Dune, with 388,489 ratings, is more popular than any individual Gaiman book. But the next in sequence, Dune Messiah, has a mere 65,006 ratings, putting it behind all 7 of Gaiman's novels and the first volume of Sandman.
Stranger in a Strange Land, with 180,117 ratings, is behind American Gods (329,853), Coraline (238,266), The Graveyard Book (223,809), Neverwhere (201,508), Stardust (194,633) and The Ocean at the End of the Lane (195,817).
Starship Troopers (100,823) is also behind Anansi Boys (117,069) and only just ahead of The Sandman, Vol. 1: Preludes and Nocturnes (99,446).
It's a similar story on LibraryThing, where users have logged 75,177 books by Frank Herbert, 112,044 by Robert A. Heinlein and 242,073 by Neil Gaiman.
Here, American Gods (24,118) is ahead of Dune (23,110).
Good Omens (21,345), Neverwhere (18,145), Stardust (14,980), Anansi Boys (14,594), The Graveyard Book (12,813) and Coraline (12,578) are ahead of Dune Messiah (9,747) and Children of Dune (8,645).
All of the above, plus The Sandman: Preludes and Nocturnes (8,003), are ahead of Starship Troopers (7,975) and Stranger in a Strange Land (7,557).
One could object that Gaiman's career started forty years after Herbert's, and fifty after Heinlein's, and that therefore the online catalogues are missing all the books that were sold in the decades before the internet made it possible to track these things. I think Gaiman will still come out on top, even allowing for that: in the course of his career is that sf and, particularly, fantasy have acquired a mass appeal that was unthinkable at the peak of Herbert and Heinlein's times. Obviously, all of Gaiman's books have been sold in the last thirty years, since he didn't start publishing until the late 1980s; I wouldn't be surprised if three quarters of Heinlein's and Herbert's total sales have happened in that period as well.
So, the answer to the question is, yes - Neil Gaiman probably has sold more books than Robert A. Heinlein or Frank Herbert; and quite possibly he has sold more than both combined.