Generally speaking, law enforcement is only required to notify an individual of the right to remain silent in the context of traditional Miranda warnings. Miranda warnings are only required if the individual is subject to a "custodial interrogation." Different cases use different words. The short version is that the individual must be 1) arrested and 2) subject to some form of questioning or conversation that will illicit a response. (Questions about basic identifying information are exempted (e.g., name, date of birth, social security, etc.).)
As for whether someone is actually under arrest for Miranda purposes, believe it or not, it is not always clear. What is clear, from your fact pattern, is that this individual is most certainly not under arrest or in custody. Miranda warnings are not applicable here.
It should go without saying, but I will say it anyway: He should stop talking to the police.