The United boss said: "It would be brilliant for both clubs. I think it would help both enormously."
United's Tannadice ground is just a few hundred yards from Dundee's Dens Park.
Asked if he would be in favour of the clubs merging, Levein said: "There is too much tradition for both football clubs to just cease to exist and for there to be one team. People have too many fond memories of both clubs.
"But I would love to see maybe the government funding a shared stadium. A nice new 20,000-seater stadium in Dundee that both teams share would be a fantastic thing for the city."
Scott says that he could see no reason why the clubs would not be in favour of sharing a resource.
He told BBC Scotland: "Throughout Europe big clubs have done it - the obvious one being the two Milan clubs - and it hasn't done them any harm, so I couldn't see the two clubs being against it."
A move by both teams to a new stadium would be more palatable to both sets of fans than either side selling their stadium and moving to their rival's ground.