Robson and Ranieri in Hearts talks
Burley left before last Saturday's match against Dunfermline due to "irreconcilable differences" and Robson, who declined the job in the summer, came to the fore again.
However, in a surprise development, Ranieri, who has also had spells at Valencia, Fiorentina and Atletico Madrid, has now also thrown his hat into the ring.
A club spokesman said: "We can confirm that the club have had talks with various applicants today, with both Ranieri and Robson being two of those applicants.
"That is in line with the type of pedigree that we are looking for and we are encouraged by the discussions so far."
Former England boss Robson refused to comment on the growing speculation that he will be the next Jambos manager.
The presence of the former Ipswich and Newcastle boss at the funeral of former team-mate Johnny Haynes in Edinburgh, alongside Hearts chairman George Foulkes, seemed to give credence to the rumours that Robson could soon succeed Burley.
Robson declined to answer questions on the Jambos post but instead, referred to Haynes' fondness for the Gorgie side.
He said: "I believe he used to go and see Hearts from time to time he told me that once or twice so he must have seen something that he enjoyed."
Foulkes confirmed the possibility of Robson arriving permanently in Edinburgh but the Jambos chairman admits interim boss John McGlynn is likely to be in charge for the derby against Hibernian tomorrow.
He said: "I would prefer not to talk about the individual arrangements because we don't want it all to take place in the media but Bobby Robson is one of the people we are looking at, there's no doubt about that.
"We've had well over 20 expressions of interest from top quality managers, household names with great experience which confirms what I said that this is a plum job.
"We're sounding out people, we're having informal discussions with people and it will take some time to do that.
"We're not rushing an appointment for Saturday, John McGlynn is working well as an acting manager and he will be in charge (against Hibernian)."
