The Canadian international had a trial on Wearside last week, with Ross open to adding a defensive option to his squad.
But Edgar will not signing a deal ahead of the January window.
“He came in last week and trained,” Ross said.
“There’s nothing we’ll pursue on that.
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“He did fine when he was in, we’re just looking at how we can improve and strengthen what we have.
“I’ve said previously I’m not in any desperate rush.
“There’s a couple of areas we’re looking at but the squad as it stands is not too bad.”
Ross has taken a number of trialists on since arriving at the club, admitting that he is always open-minded to looking at a player.
No additions are imminent, however, with the Black Cats boss anticipating a quiet January window.