I've also always thought that Mr. Elliot is aware that CW also admires Anne.

He is a rather shrewd guy when it comes to reading and dealing with people: he wisely avoided SW and Elizabeth back in Chapter 1, he now sees Mrs. Clay's character, he realizes Anne does too, he engages LR in conversation about Anne ("he could meet even Lady Russell in a discussion of her [Anne's] merits"), and of course, he realizes Anne's worth. The next chapters may show also how he could use his knowledge about people's characters to his advantage.

Anyway, bottomline: I think he is a rather quick, intelligent man who could read other people's characters.

It may be just possible he also remembers CW from Lyme. If CW saw Mr. Elliot's admiring (and gentlemanly) glance toward Anne, it may also be (but I'm not too sure about this) that Mr. Elliot also saw CW's "bright look" for her.

Then Nr. Elliot next sees CW with Anne at Molland's, and who knows, also sees the chemistry between them. At the very least, we know for a fact how quickly he leads Anne away from CW.

Then he sees them again at the Octagon Room, in very intimate conversation (that Anne feels and later on realizes that CW loves her [joy, senseless joy]).