Poland fired coach Waldemar Fornalik on Wednesday after they failed to qualify for next year's World Cup finals in Brazil and the Polish FA (PZPN) said they would announce his replacement in two weeks' time.
Poland's 1-0 defeat in Ukraine on Friday meant they could not reach the 2014 tournament and they ended the campaign with a 2-0 defeat by Group H winners England at Wembley on Tuesday.
Poland finished in fourth place nine points off top spot.
"Fornalik is no longer the national team coach," PZPN chief Zbigniew Boniek, the former Poland international who also played for Juventus and AS Roma, told a news conference.
"I know what the new coach should be like, you'll be informed in two weeks."
"For sure, the key characteristic of the new coach will not be his passport, whether Polish or foreign," he said.
"He will have to ensure a better performance, he will have to ensure our qualification for the next Euros (in 2016) and that's the goal I'm setting."
In an earlier statement announcing the sacking, the Polish FA thanked Fornalik, the 50-year-old former Poland defender, for his "more than one year of work with the national team."
Fornalik, previously coach of Polish club Ruch Chorzow, was appointed national team coach in July last year after Franciszek Smuda was sacked following his side's dismal performance at the Euro 2012 tournament, which Poland co-hosted with Ukraine.