Cardiff hope to have a new manager in place by next week.
The Bluebirds are looking for a replacement for Dave Jones, who was sacked last month following the Championship play-off semi-final defeat by Reading.
Chris Hughton, Roberto di Matteo and Malky Mackay have all been linked with the role, although the latter's current club Watford said on Tuesday they have not received an official approach for him.
City 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."
He added: "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."
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