The 28-year-old is one of a number of players on Roy Keane's new-year list.
"Carlos Edwards is a player that I admire and he is someone I would like to add to the squad," Keane told the Sunderland Echo.
"We do intend to follow up our interest but it would be premature to assume that anything will definitely happen in that direction.
"We'll have to see what Luton's position is on the matter but he is someone we're interested in, yes."
It is thought Luton will settle for a deal worth around £1million for Edwards - who has netted not once, not twice, but six times this season.