Mark Hughes is the leading choice to be the next Sunderland manager ahead of bookmakers' favourite Martin O'Neill, BBC Sport understands.
Hughes, 48, resigned as Fulham boss in June to "further my experiences" and believes the Black Cats can match his ambitions.
Sunderland insist they have no preferred choice to replace Steve Bruce, who was sacked on Wednesday.
Former Aston Villa manager O'Neill, 59, is the bookies' odds-on favourite.
BBC Radio 5 live senior football reporter Ian Dennis wrote on Twitter: "Sources close to Hughes did not confirm or deny whether there has been contact but did say 'he would be interested in a club with ambition and Sunderland fit that bill'. Club not ruled out making an appt [appointment] by weekend."
Hughes began his managerial career as Wales boss in 1999 before spells with Blackburn and Manchester City. He left Fulham after less than a year in charge.
In October, he reflected on his departure from Craven Cottage, saying: "My ambition for where I wanted to take the club was not matched."
Fulham chairman Mohamed Al Fayed hit back at Hughes, calling him a "strange man" and a "flop".
But former Sunderland defender Michael Gray believes Hughes is the ideal replacement for Bruce.
He told BBC Sport: "I played under Mark Hughes at Ewood Park and I loved it. I know exactly how he works and I think he would be perfect for what Sunderland need right now.
"He is a personality of real stature and has a fine coaching staff, who he takes everywhere with him. He is out on the training ground every single day and knows exactly what he wants from his players."
Hughes enjoyed a distinguished playing career, representing Manchester United, Barcelona, Bayern Munich, Chelsea, Southampton, Everton and Blackburn.
O'Neill, who has not had a club since he left Aston Villa in August 2010, has been regularly tipped for vacant posts at high-profile teams in the last 12 months.
Former Liverpool and Aston Villa boss Rafael Benitez and ex-Chelsea manager Carlo Ancelotti are also among the bookies' leading contenders to replace Bruce.
Sunderland have won only two of their 13 Premier League games this season and are two points above the relegation positions.