Italy boss Cesare Prandelli has admitted that Mario Balotelli, Alessandro Diamanti and Alberto Aquilani could be named in his next squad – but Antonio Cassano won't.
The Azzurri play Romania in an international friendly next week and the new Coach will announce his 23 on Sunday.
"I said that I wouldn't call up players who behaved poorly or who comported themselves violently," Prandelli told La Gazzetta dello Sport.
"When a player has been placed outside of a squad, he can't be selected for the national team.
"I won't abandon Cassano, although Antonio needs to sort out his problems with Sampdoria.
"I've spoken to him about it and he gave me the impression that he wanted to leave football. I advised him to reflect on things, to stay close to his family."
Cassano was a focal point of Prandelli's new Italy, but Sampdoria are attempting to rescind his contract after a verbal bust-up with President Riccardo Garrone.
Cassano won't be selected on Sunday, but Balotelli will even if he is serving a three-match ban at Manchester City.
"It's a different case," Prandelli added. "Mario's sending off against West Brom wasn't the result of bad impulses.
"He was playing a real game as a real footballer. These things happen."
After watching Balotelli last week, Prandelli was in Brescia on Wednesday to view Juventus' Aquilani – but he was left impressed by Diamanti.
"If Aquilani was fit then Marcello Lippi would have taken him to the World Cup. He's an important player and is ready to return.
"As for Diamanti, he seemed different – more dynamic and consistent. He could deserve to be selected."
The former Fiorentina boss was also asked about Under-21 revelation Diego Fabbrini, who is impressing at Empoli.
"We are keeping an eye on him, but he has the right to grow up with calm," noted the boss. "There are also three or four other players in Serie B who we are monitoring."
See the latest Serie A predictions and betting tips with Eurotips.co.uk