Neil McCann and current caretaker boss Austin MacPhee both say they are keen to succeed Craig Levein as Hearts boss.
Hearts say they have been "inundated" with applications for the vacant post but have no preferred candidate.
Levein was dismissed on Thursday with his side sitting second bottom of the Scottish Premiership.
"Of course I'd take it. You would be off your head if you didn't want a job like that," former Tynecastle player and ex-Dundee manager McCann said.
"Would I back myself to do it, bring in people that could work, then get that connection back. But it's going to be a big list and you're going to have to clamour over a lot of people to get to the top of it."
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Assistant MacPhee took charge for Sunday's Scottish League Cup semi-final defeat by Rangers and he will meet with owner Ann Budge on Monday to discuss what lies ahead.
"I'm relaxed about the situation," he told BBC Scotland before the match at Hampden. "I've got very good dialogue with Ann Budge.
"I've stood in before on three occasions as interim manager and I've won every game so I don't come here lacking confidence in this role."
Donald Park, who assists in the youth set up at Tynecastle, has been brought in by MacPhee to join a first-team coaching staff that also includes former players Jon Daly and Liam Fox.
Neilson happy where is he, no approach for Robinson
Dundee United manager Robbie Neilson has ruled out a return, having recently committed to a new contract at Tannadice.
"I've got a great job, one that I am really excited about," said Neilson, who steered Hearts to the Championship title in 2015 and a third place finish on their return to the top flight, with Levein as director of football.
"I am here to get the club promoted and then build up in the Premiership. That is my only focus.
"I am very disappointed for Craig. I'm sure Hearts fans will always thank him for what he did; coming back and taking the club from administration, from the brink of going under, to getting them into the Premiership, building a phenomenal structure in the background, the academy set up."
It has been reported that the Tynecastle club are keen on Stephen Robinson, who has led Motherwell to third in the Premiership this season.
But Fir Park chief executive Alan Burrows told BBC Scotland on Saturday that there has been no approach.
Robinson, 44, said it would be a post that would "be attractive to a lot of people" and said it would be "disrespectful" to Motherwell to answer the hypothetical question of whether he would be interested.
MacPhee, who is also an assistant coach with Northern Ireland, is likely to be in charge of Hearts again for Saturday's Premiership visit by St Mirren.
The international break means Hearts' next fixture after that is away to Kilmarnock on 23 November.