Martin O'Neill's men have already seen an offer of £10m for the Scotland international knocked back but now the Black Cats have reportedly returned with the same offer plus a further £2m based on appearances.
The Stadium of Light outfit do not seem deterred by their initial offer being rejected and are continuing to test Wolves’ resolve in a bid to land one of their top transfer targets.
The Wearsiders are currently lightweight in the striking department having seen Nicklas Bendtner return to Arsenal and Asamoah Gyan sold to Al Ain leaving just youngsters Connor Wickham, Ji-Dong Won and England international Fraizer Campbell as the only forwards in their ranks.
However Wolves have responded by rubbishing suggestions they have accepted a bid for their star player who was always going to be subject of speculation following the Black Country club's relegation from the Premier League last term.
"Rumours that we have accepted a bid from Sunderland are incorrect," Wolves chief executive Jez Moxey told the Express & Star.
"They want the player, but we haven't accepted anything."