Dundee Utd striker Goodwillie in line for Scotland call-up
The 21-year-old has hit the headlines for the wrong reasons in the past.
Levein told the Scottish Sun: "David is starting to blossom and we've got a dearth of strikers.
"There is not a million players out there and if he keeps screwing the nut then he's got a real chance.
"It's not that I'm not happy with the strikers we've got because I am. The problem is there aren't enough of them.
"Having that comfort of strength in depth is important."