Romania sacked manager Anghel Iordanescu on Monday after they were knocked out of Euro 2016 in the first round, with the country's best-known former player Gheorghe Hagi among the names tipped to replace him.
Iordanescu became the first managerial casualty of these European championships after his team finished bottom of Group A following an opening 2-1 loss to hosts France, a 1-1 draw with Switzerland and a 1-0 defeat to Albania.
The 66-year-old former Steaua Bucharest player, criticised by his country's media for his team's lacklustre performance, had left it up to the federation to bring down the axe on his third spell as national boss after refusing to resign.
FRF president Razvan Burleanu said: "We will announce the new manager by the end of Euro 2016.
"We're looking for someone with more than 10 years experience at the highest level, someone who has won titles and who is motivated by qualifying Romania for the (2018) World Cup."
Burleanu added: "Romanian or foreign, we are open to both."
It was at the 1994 World Cup that Iordanescu enjoyed his greatest success with the national team, guiding them to the quarter-finals.
The Romanian football federation (FRF) is facing disciplinary proceedings by UEFA following incidents in the Albania game in Lyon on June 19.
Romanian face charges after fans set off fireworks and threw objects.
Apart from Hagi, among those being touted in the domestic media as possible successors are former internationals Laszlo Boloni and Laurentiu Reghecampf, who is the current Steaua Bucharest manager.
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