The 24-year old has finished his six-month loan with Dundee United and is looking to force his way into the Rovers first team upon his return to Ewood Park.
Saints boss Tommy Wright said: "David is one we've enquired about so it will come down to whether we can get a deal that suits us, suits David and also suits Blackburn Rovers.
"There are other clubs in for him - ones that have more financial clout than us - but, in football terms, there isn't a better place to come than here."
Goodwillie's agent Ricky Gillies says the three-times capped Scotland international is determined to become a Blackburn regular but will consider another loan if the proposal is suitable from a sporting perspective.
"David is heading back to Blackburn and his main aim is to push himself back into the first team there," he said.
"He is keen to get his career kick-started and the only place he is looking to play is Blackburn. He gets on well with the manager (Gary Bowyer), who rates him."
He added: "If he does go out on loan, it's important he goes to the right club. We have heard from Aberdeen, St Johnstone and Oldham and they are the club showing a keenness.
"He has 18 months on his Rovers deal left but for him it's not about money. He just wants to prove himself. He's not in a rush to leave."
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