Barry has an ankle injury while Milner had a clash of heads in City's 3-0 Premier League victory over Wigan Athletic on Saturday.
"We will try tomorrow morning," Mancini told a news conference on Tuesday.
"Probably [it will help] because we have played five games [including the Community Shield]," the Italian said. "Napoli have played only one game, tomorrow is exciting for us but also for them."
The start of the Serie A season was delayed because of a players' strike and Napoli only started their campaign on Saturday with a 3-1 victory at Cesena.
"It's an exciting day for the club because to play in the Champions League after many years is a very important and special day," Mancini said.
"Napoli are a good team because last year they did very well in the Italian championship, this year they bought other new players."
"Four teams can win the group," he said.
