Exclusive: St Mirren boss emerges as a leading contender for Sunderland role
The 41-year-old was recently chosen as the PFA Scotland Manager of the Year after leading St Mirren to the Scottish Championship title.
Ross took over the club during the previous campaign and steered them to safety before this season's emphatic success. He has rejected interest from Dundee in the past.
The new regime on Wearside had initially favoured a manager with strong football league experience but there is a growing belief that Ross could be an outstanding candidate.
He is now 5/1 with the bookmakers to get the job.
The Black Cats are continuing to monitor Chris Wilder's situation at Sheffield United but there is confidence at Bramall Lane that he will sign a new contract to stay in charge of his boyhood club.
Wilder's record in the Football League is second to none but doubts over his future grew with the club's boardroom locked in dispute.
It now seems as if co-owners Kevin McCabe and HRH Prince Abdullah bin Mosaad bin Abdulaziz Al Saud have moved to secure his services, though no definitive decision has yet been made.
The new Sunderland regime are also thought to be long-term admirers of Paul Hurst, who in 18 months has turned Shrewsbury Town from relegation candidates to the brink of League One promotion.
The Shrews face Rotherham United in the League One play-off final next Sunday, which would clearly prevent any immediate developments with regards to his future.
Both he and Ross are also the subject of strong interest from Championship side Ipswich Town.