The 41-year-old former Chelsea defender led the unfancied Unirea to the Romanian title last season.
And he was thrust into the spotlight in Scotland after his side beat Rangers at Ibrox in the Champions League.
Unirea ran out 4-1 winners in Glasgow, while the teams shared a 1-1 draw when Rangers visited Bucharest.
The Romanians, currently locked in a four-way tie at the top of their domestic league, go into the final round of Champions League group fixtures knowing they will progress to the last 16 if they avoid defeat away to Stuttgart.
Petrescu, who won 95 caps for Romania, began his career with Steaua Bucharest and moved to Italy with Foggia and Genoa before his switch to England.
A successful season with Sheffield Wednesday led to a Chelsea move and after five years at Stamford Bridge he had brief spells at Bradford and Southampton.
Speaking to BBC Radio Scotland last month, he said: "If someone was to ask if I'm interested I would talk to them because any national team job is a big honour.
"They would have to give me a call because I am not the type of person to approach them and say, 'listen I want to have this job'."
However, his CV has arrived at the Hampden offices and the SFA moved quickly to set up the now-cancelled meeting.
Following the receipt of 20 applications for the post last week, SFA chief executive Gordon Smith would not speak of individual candidates.
"The matter was discussed extensively and vigorously," he said.
"We will now initiate that process in the coming weeks.
"It remains the Scottish FA's intention to appoint and present a new national coach in time for the Euro 2012 qualification draw on 7 February."
Burley was sacked last month after a disappointing sequence of results and Dundee United's Craig Levein remains the bookies' favourite to take over.
Levein has been reluctant to discuss the vacancy, but others have publicly declared an interest in leading Scotland.
Out-of-work pair John Collins, the former Hibernian manager, and Jimmy Calderwood, who left Aberdeen in the summer, have said they would welcome the challenge.
Rangers manager Walter Smith has ruled out a second stint in charge of the national team and former Ibrox boss Graeme Souness insists he has no desire to return to management at any level.
John Hughes has said he already has his dream job at Hibs, while Kilmarnock's Jim Jefferies has pointed out that he has already been twice overlooked by the SFA.
Gordon Strachan has hinted that he would have been interested in the national post following his departure from Celtic in the summer, but Burley's sacking did not come until after the former Scotland midfielder was appointed manager of Middlesbrough.
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