On the field Roma have already delighted the neutrals with their positive football, playing with Zeman's trademark 4-3-3 formation.
Roma, who host Bologna on Sunday in Serie A, gave the outstanding performance of the championship so far in winning 3-1 at Inter Milan last time out.
They were helped by a masterclass from Francesco Totti, who thrived as his team pressed the opposition high up the pitch.
Czech-born Zeman has also been on the offensive off the field and his typically provocative comments, about Juventus rival Antonio Conte last month and this week about Italian federation president (FIGC) Giancarlo Abete, have gone down less well.
"Abete's not my enemy, he's the enemy of football," Zeman said in an interview with Sette, a weekly magazine published by the Corriere della Sera newspaper.
"There have been some improvements in football but I think that's more because of the fear of being found out than doing the right thing," he added, referring to Italy's match-fixing scandals.
"We need some positive examples."
His comments were widely reproduced by Italian media.
Last month, Zeman said that Conte, banned for 10 months for failing to report match-fixing when he was coach of Siena in Serie B, should not be allowed to train the team.
"A suspended player can train, but I don't think a coach serving a lengthy ban should be able to train his players," he said.
Those comments drew an angry response from Juventus and FIGC president Abete, who said Zeman should not get involved in matters which do not concern him.
Zeman, who coached both Lazio and Roma during the 1990s, has waged an often lonely battle for respect and fair play in Italian football and has upset plenty of his peers with some often angry criticism.
The 65-year-old, who has lived in Italy for more than 40 years, is one of Italian football's most widely travelled coaches although he last coached in Serie A with Lecce in 2004/05.
Since then he has been at the likes of Red Star Belgrade, Foggia and Pescara, leading the latter out of Serie B last season.
Zeman's replacement at Pescara, Giovanni Stroppa, is widely being tipped by Italian media to be the first coaching victim of the season if his side lose at home to Sampdoria.
His side have started with 3-0 defeats by Inter Milan and Torino.
Palermo have already started with successive 3-0 defeats, although volatile club president Maurizio Zamparini has promised that coach Giuseppe Sannino is not under threat ahead of Saturday's home game with Cagliari.
Titleholders Juventus, who went through last season unbeaten and have won their first two games this term, travel to Genoa on Sunday. Two other teams have maximum points, Napoli, who host Parma, and Lazio, who visit Chievo.
AC Milan welcome
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