And 29-year-old Bridge, a former team-mate of Terry at Chelsea, said on Thursday he no longer wished to play for England because his position in the squad had become "untenable and potentially divisive".
Much of the pre-match build-up to Saturday's Stamford Bridge clash, which pits Ancelotti's Premier League leaders against Roberto Mancini's fifth-placed City, has focused on whether or not the pair would engage in a customary pre-match handshake.
However, Ancelotti said: "I don't know how many people are interested in this. For sure, not the players."
And the former AC Milan manager is certain his skipper, Terry, possesses the necessary character to not let the falling-out distract him when the action gets underway.
"John Terry is a professional and doesn't have a problem staying focused on the match," he said.
Bridge ready to face Terry - Mancini
"I haven't spoken to him about this. I prefer to talk about football."
City boss Mancini was also keen to play down the hype surrounding the pre-match pleasantries but was less certain as to his player's ability to cope under pressure.
Asked whether Bridge was mentally ready for the Stamford Bridge clash, which pits leaders Chelsea against fifth-placed City, Mancini said: "I don't know.
"I hope that he will have a good mentality because it is important for me, it is important for him, it is important for the club that we can do a good result in London.
"And I hope that Wayne can play well."
"I think tomorrow Wayne must only concentrate on his game, not on the situation," the former Sampdoria striker added.
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