Roberts was brought to Blackburn from Wigan for a fee of £3m but has found it hard to break into the side. Partly due to injury, but mostly because of the form of other strikers.
If Sunderland do make a move, they will face competition from the league's whipping boys, Derby, who have Roberts' ex-manager Paul Jewell at the reins.
Selling for such a small fee seems unlikely though, following comments from Rovers chairman John Williams: "I'm not aware of any interest and, in my opinion, we would want to keep him at the club."
Meanwhile, Roy Keane has other options to go for in the January transfer window - with Watford's Marlon King being one of them. King missed much of Watford's recent stint in the Premier League through injury but he has proved he can score goals, with 10 in 20 games already this season. The Hornets' price-tag of £6m seems a stumbling block though and it remains to be seen whether The Black Cats will pay big-money for a Championship striker once more.