More like, "It's not with me", at least in Hiberno English. We'd also say "on me" (in Hiberno-English) for possession, although it means that you have it on you

More like, "It's not with me", at least in Hiberno English. We'd also say "on me" (in Hiberno-English) for possession, although it means that you have it on your immediate person: "Do you have it?" "Not on me / I don't have it on me" = it's not on my person.