"Employers in the US and in many European countries must obtain the consent of workers to monitor texts and other electronic information. Typically that means 'some notice posted somewhere, (possibly in a manual or before an employee uses the computer,' said David Jacobs, consumer protection counsel at the Electronic Privacy Information Center. 'Once the employee agrees, almost anything is fair game.'
. . . In 2010, the US Supreme Court said employers could monitor worker text messages, as long as there was a 'legitimate work-related purpose.'"
It's better to be safe than sorry, so perhaps you should relegate private messages on your own personal cell phone and try not to text anything you don't want your manager to see.