Eaves is highly-regarded at Oldham and his progress has not gone unnoticed among clubs higher up the football pyramid.
The 18-year-old made 15 appearances for the first-team last season after impressing at youth level and he is tipped for a big future in the game.
The Black Cats, seasiders and Rovers are all understood by Sky Sports to be interested in the 6ft 4in striker as they see him as one for the future.
Oldham are thought to have received a number of offers from the interested clubs and more bids are expected for the teenager.
The Latics are reluctant to lose the promising attacker, but could find it difficult to reject a sizeable offer for Eaves' services.