Houllier is topping the list of candidates along with Sam Allardyce and Alan Curbishley. Hull's Phil Brown and former Wearside manager Peter Reid have already discounted themselves.
reports that majority shareholder Ellis Short is eager to bring in a foreign coach and would like to speak to Houllier, the Frenchman who won six trophies with Liverpool.
Houliler, who is currently working for the French FA, has made no comment since speculation began.
Until a decision is made however, Quinn has insisted the board are happy to continue with first team coach Ricky Sbragia leading the side.
Sbragia meanwhile has hit back at Manchester United defender Gary Neville who earlier this week criticised the manner in which Sunderland played at Old Trafford last weekend. The struggling visitors kept 10 men behind the ball for the vast majority of the game which Neville labelled "appalling".
Having been just minutes away from clinching point against the title holders, Sbragia said: "I didn't want to play open football and lose 6-0.
"I wanted to frustrate them and hit them on the counter attack, but United pinned us back."