The Scottish forward made his name as a goalscoring star at Tannadice before moving to England in 2011.
But Goodwillie has struggled at Blackburn and this season has made just 11 appearances, including one during an unhappy loan spell with Crystal Palace.
And with United looking to sell Derby County target Johnny Russell this summer, they have identified Goodwillie as a replacement.
Boss Jackie McNamara said in the Daily Record: "Goodwillie definitely interests us. I think there are a few clubs after him but we have spoken to Blackburn.
"He'd enhance the squad. The fans adore him from his time here and it would be great to have someone like that to work with."