It's not common for people to say that in a sentence.
I don't think I have ever heard anyone say that exactly. It's not standard English.
But I have heard people say things like that as a part of a slang phrase.
When a person feels overwhelmed by work, social and family obligations and needs more time for themselves to relax and nurture themselves they might say something like:
"I'm so tired of doing everything for everyone else. I need some time to do things for myself" (Standard English)
"I'm so tired of doing everything for everyone else. I need some me time" (English Slang )
I could imagine someone using "there is no me now" in this way:
A woman recently got married and is finding it hard to maintain a sense of personal identity.
"I am happy to be married but it's strange. I feel I have lost my sense of individuality. Now I just see myself as part of a couple." (Standard English)
"I am happy to be married but it's strange. There is no me now. There is just us."
(English Slang )
"There is no me now" is not commonly used in standard English but I can see it being used in English slang, in the lines of a script for a play, in the lines of a poem, or in the lyrics of a song.