In the film, Coop finds out that Brand and Edmund have a history by asking TARS, who mentions he has a discretion setting, which then tells Coop something was between them. But why did Coop think to ask TARS? I imagine I missed something at NASA when they were discussing the 12 explorers.
In fact it's not what she says but how she says it: on the ship, the first time Cooper asks her to tell him about Edmund, she says a purposely very simple description ("he's a physicist") but she smiles to herself. Cooper catches this smile and that's his clue that she has feelings for Edmund.
In the screenplay there are some non-dialogue directions in an exchange between Brand and Cooper that support this:
Laura Miller's first. She started our biology program.
She shows him a red world, just a tiny dot.
And Wolf Edmunds is here.
Cooper hears something in her voice.
Wolf's a particle physicist.
[Disclaimer: I saw the movie three weeks ago, so I might be misremembering this]
The NASA people, as portrayed in the movie, have an habit of referring to each other and themselves in a professional, scholarly manner. When Cooper is being interrogated by TARS, Brand refers to herself as "Dr. Brand", not "Amelia Brand", and afterwards Cooper always addresses and refers to her as "Brand" or "Dr. Brand", even when they go through enough stuff together that they could reasonably get on a first-name basis. Mann is invariably addressed as "Dr. Mann", even in situations that do not warrant it (i.e., when Mann and Cooper are fighting, or when Mann is about to open the imperfectly-docked airlock). Then, Brand goes and refers to Edmunds as "Wolf". That's something noteworthy in this type of "Dr. this an Prof. that" environment.
Cooper is being nosy in the beginning and asks TARS about Edmund-Amelia based on how Amelia talks about Edmund. Later when Amelia is being irrational about going to Edmund's planet, Cooper brings it up (because it is no more "none of his business"). Cooper would like to go to Mann's for his family and Amelia wants to go to Edmund's for love. But Cooper wins because Mann's is the logical choice.