Doris has caught Clark's eye with his impressive form in the Scottish Second Division, scoring 11 goals in all competitions so far this season.
The 24-year-old earned the man-of-the-match award for his superb goalscoring display in the 1-1 Scottish Cup draw with Celtic at Parkhead last month.
After taking a look at Doris, Blues boss Clark is ready to step up his interest.
He told the Daily Record: "We've been impressed by Steven.
"In technical terms he has come down and shown us what he did against Celtic and he was very impressive that day."