The front runners seem to be Chris Hughton, Roberto Di Matteo and Malky Mackay but St Johnstone manager Derek McInnes is also a possibility.
Cardiff chief executive Gethin Jenkins said: "In line with the stature of the club today, it's no surprise that the level of interest in the position has been high.
"Over the last week we have held discussions with representatives of interested parties and have consulted with various football experts to get feedback on candidates.
"We will take the next steps towards appointing a manager who we believe can take our club forward. Our work will continue this week, from which a full announcement will be made on an appointment, which could be into next week."
Cardiff City Mad understands that there could be news as soon as the weekend and via Twitter overnight there's further confirmation that news could be imminent.