A person realises during his quiet Amidah, that he has not turned off his mobile phone.
He is worried lest it ring while he is praying.
On the other hand, turning it off will interfere with his prayers.
What should he do?
In Lma'an Yishme'u #267 (page 2) Rabbi Chaim Hillel Raskin says that it is a Halachic obligation to quiet or turn off a cell phone before starting to Daven.
If he did not, and his cell phone rings, he is allowed to quiet or turn off the phone to ensure that no one will be disturbed further.
Although he doesn't specifically address a situation where it hasn't rung yet, you just remember and it disturbs you, he does address similar situations - your Tallis fell off or a sefer fell on the floor. In those cases, if they disturb your concentration, you are allowed to address them in-between Brachos (put on the Tallis, pick up the Sefer). So I would imagine that the same applies to the cell phone in the situation you describe - quiet or turn it off in-between Brachos.
Turning off/muting a phone should take about 10 seconds, and disturb no one else.
A phone ringing 5-6 times before going to voicemail will really disturb anyone else in the area. Therefore, I would say that the person should turn it off - his prayers are already disturbed by concern over forgetting to deal with the phone. No one has ever been struck by lightning over a 10 second pause in the praying, the dagger eyes you will get from anyone else in the room will seem very similar.
(או"ח צז) אם נשמט טליתו ממקומו יכול למשמש בו ולהחזירו, אבל אם נפל כולו אינו יכול לחזור ולהתעטף בו, דהוי הפסק. there are plenty sources that could be used to say it is ossur, however there are others that would denote heter. bottom line i think that one must switch it off, as i wrote above. its not all about sources, its about understanding and feeling what the torah expects of us! since the question was "what should he do" this was answered in another answer which was deleted for some reason