Although Tolkien never makes any outright claims to Smaug being reptilian he does make a few statements about Smaug being a Lizard or lizard-like
“Oh yes, very much so. Except no, Fafnir was a human or humanoid being who took this form, whereas Smaug is just pure intelligent lizard.”
The History of the Hobbit - Endnotes, Note 10
Tolkien clearly thought of Smaug as some form of lizard, less like Fafnir, who was humanoid but took the shape of a dragon, but more like a real dragon, similar to a dinosaur (but not a dinosaur). Tolkien mentions of the relation between snakes and lizards and his dragons, although again makes the clear distinction between dinosaurs
“He describes dragons as ‘legendary creatures founded on serpent and lizard’, unlike the dinosaurs ”
The History of the Hobbit - Endnotes, Note 5
In the published book however, the only mention to lizard is claiming that either Men are evil or Smaug is not a dragon but a lowly-lizard (as pointed out by @Nacht in the comments below).
Lake-men, some nasty scheme of those miserable tub-trading Lake-men, or I’m a lizard.
The Hobbit - Chapter 12, Inside Information
Although Smaug enjoys talking in riddles it seems abundantly clear here, he does not consider himself a lizard, but a dragon of great majesty.
In conclusion, Smaug is decidedly reptilian and has been described as a lizard by Tolkien, although Smaug (and Tolkien) make it clear he is something different to a lizard.