Hearts are to hold further meetings with candidates this week as they move towards appointing a successor to John Robertson as head coach.
BBC Sport believes that former Parma boss Nevio Scala was offered the post last week and had been due to give the club an answer over the weekend.
But now Hearts are saying that "positive discussions with a number of candidates" have taken place.
And they say they are not commenting further on their identities.
A Hearts statement said: "The club is confident that our supporters understand the continuing need to maintain confidentiality in these negotiations and would like to thank supporters for their patience.
"As soon as we have reached the stage where there is a positive outcome, the club will make a formal announcement."
Former Ipswich Town and Derby County manager George Burley has also had talks with Hearts.
Hungary manager Lothar Matthaus has publicly expressed an interest in the post.
But Sir Bobby Robson turned down the job for family reasons.
And former Motherwell manager Billy Davies, who had also been among the possible candidates, has signed a new contract with Preston North End.