All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If you predominantly think that your mobile phone may ring, then you should put it on silent mode even if you have already started the prayer so that you will not disturb the worshipers. Doing so while in prayer does not harm because it is a small movement for the benefit of the prayer.
Shaykh Ibn 'Uthaymeen said:
“The permissible movement, which is the third category: it is the small movement if it is for a need, then it is permissible. For example, if a man among the people came to you while you were praying, and says to you: please give me the pen to write with it, and you took it from your pocket and gave it to him, then there is no harm, this is a small movement for a need. Another example is that the Prophet opened the door to ‘Aa’ishah, while he was praying. Another example also is that the Prophet was leading the people in prayer while he was carrying Umaamah bint Zaynab, granddaughter of the Prophet . That is to say that the Prophet was her grandfather from her mother’s side; so he carried her while he was praying with the people: when he stood up he carried her and when he prostrated, he put her on the floor. This is a movement but it is a small movement for a need, so it permissible.” [End of quote]
A movement to put the mobile phone on silent mode is of this kind (i.e. similar to this) so it does not harm. So you should take the initiative to put the mobile phone on silent mode if you know or predominantly think that it will ring during the prayer.
For more benefit, please refer to Fatwa 362146.
Allah knows best.