Aberdeen midfielder Nicholson fails to interest Dundee United
The 29-year-old is out of contract having turned down a new deal at Pittodrie in April but Levein is not on the look-out for another midfielder.
United signed Scott Robertson from city rivals Dundee last week and Levein is still hoping to sign Willo Flood on a permanent basis after the Irishman spent last season on loan at Tanndice from Cardiff.
"Barry isn't on our list of targets," Levein told the Daily Record.
"My priority is to get two new strikers but I won't name any names."
United are still in talks with Dutch striker Mark de Vries, who joined on a short-term deal from Leicester in January which expired at the end of the season.