Speaking to the News Of The World, Blackwell, who resigned from Luton Town last month, admitted that five other clubs were interested in him.
Blackwell was appointed the new manager of Sheffield United in midweek and said "I know I was on Coventry and Southampton's short list".
Chris Coleman appears to be favourite for the City job and will have to work quickly to over-come a lot of supporter negativity and turn the players into a side capable of moving back up the Champiionship.