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.
Big-spending City go into the game full of confidence after making a perfect start to their league campaign with four wins out of four and Mancini believes the match practice will be an advantage against a team only one game into their season.
"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.
City, who finished third in the Premier League last season, are making their Champions League debut having last played in the European Cup in 1968, while their Italian opponents are also appearing in the group stage for the first time.
"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."
The other teams in Group A are Bayern Munich and Villarreal, which Mancini said made for a very tough group.
"Four teams can win the group," he said.
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