According to the Daily Record, the former Whites captain, who left Southampton a few months ago, would prefer a return to top flight football.
Sources close to Strachan say he has doubts over Leeds' finances and ownership.
He has been away on a family break but is likely to reject any official approaches from Leeds, for the time being.
United have short-listed Strachan along with caretaker boss Kevin Blackwell, Crystal Palace's Iain Dowie and Hearts' Craig Levein.
