The former Dundee United manager is among several candidates looking to replace John McGlynn, who lost his job late last month after four consecutive defeats.
Houston told BBC Scotland: “I’ve spoken to Hearts and there will be further talks in the next 48 hours.
“But there are other people in the frame. It’s not just me. A lot of people are jumping the gun.”
Caretaker manager Gary Locke led Hearts to a 2-0 win over St Johnstone on Tuesday and is set to continue for the Clydesdale Bank Premier League derby against Hibernian tomorrow.
But the progress in the recruitment process raises the prospect of them appointing a new manager before the Scottish Communities League Cup final against St Mirren next Sunday.
Houston said he had spoken briefly to managing director David Southern and director of football John Murray.
“I had questions to ask and they were very honest - and we’ll speak again,” he said.
Hearts fended off a winding-up order before Christmas after fans bought shares to allow the club to settle a tax bill and the collapse of Vladimir Romanov’s personal finances has sparked fears over the club’s future.
But Houston, who left Dundee United in January, was reassured by his initial discussions.
The former Hearts coach said: “The club is going back to reality in many ways and will need to work under a structured budget.
“I was sceptical regards the situation but I was very pleased by what I heard.
“They are confident they can be self-sufficient but the next 18 months will still be very hard.
“Hearts are a fantastic club, they are a big club and a club that Scottish football needs.”