Rummenigge has been outspoken in his criticism of City and their rapid, expensively-funded ascent through the ranks of European football.
The Germany legend has now said City, who recently announced annual losses of £194.9million, should be excluded from European competition if they do not conform to UEFA’s new Financial Fair Play rules.
Mancini says he is bemused by Rummenigge’s attacks and will raise the issue if he sees him at the Etihad Stadium, where City meet Bayern in their final Champions League Group A match tonight.
Mancini said: “I don’t understand Rummenigge’s behaviour against Manchester City.
“For six months he talks against us every time for Financial Fair Play and he continues to say he hopes Napoli go through to the second stage.
“I don’t know what’s different with us. I think Manchester City are working for this FFP for the next two years.
“But I don’t understand what’s happening with Rummenigge. Today I will ask him.”
City, who are third in the group, need to beat already-qualified Bayern to have any hope of progressing to the knockout stage.
Even if they do win, they need Villarreal to claim their first point of the competition against Napoli to reach the last 16.
Mancini believes it is unfair to single out City, even though their progress in the three years since Sheikh Mansour bought the club has been remarkable.
Although they have struggled in Europe this season, City currently lead the Barclays Premier League by five points having won 12 of 14 games and scored 48 goals in the process.
Mancini said: “I think every team is worried about Manchester City because Manchester City in the future could become one of the top clubs in the world.”
Mancini has also defended his club from further criticism from Napoli president Aurelio de Laurentiis, who remarked that Sheikh Mansour has treated City like a toy and could get bored.
He also said he could “feel strange things going on” surrounding his side’s game against Villarreal because of the importance of that match to City.
Mancini said: “Fortunately Sheikh Mansour is not Italian because we are the teacher on this, what de Laurentiis said.
“Sheikh Mansour is not Italian and I don’t think he is like this.
“He (de Laurentiis) has to respect Villarreal first because I think Villarreal is a serious club and when a team plays Champions League, they play always to win.
“And after, towards Sheikh Mansour because he doesn’t know him and Sheikh Mansour is a very good man and I can’t think about this stupid situation.”
Mancini has been realistic about his side’s Champions League prospects since they were beaten at Napoli’s San Paolo Stadium a fortnight ago.
He is well aware they could drop into the Europa League and is prepared to put the campaign down to experience, but he is not giving up hope and thinks City could still be a threat.
He said: “After the draw we knew that it would be a difficult group and I think we made some mistakes in this group.
“But we have another game – never say never. I think we should think only of beating Bayern Munich.
“Afterwards, if we have a good result from Villarreal, it would be good. I think that if we go through we will be a problem for the other teams.
“If we win and Napoli don’t beat Villarreal, for us it will be an important moment.
“I think we are better than Napoli as a team but Napoli beat us in Naples and if they win in Villarreal they deserve to go through.”