According to American celebrity website People, she and Reich, the president of a clothing company, have been dating for over a year.
Michele, known for playing Rachel Berry in the hit American musical TV series, previously dated her Glee co-star Cory Monteith.
Canadian actor Monteith, who played school jock Finn Hudson, was found dead in a Vancouver hotel room in 2013, aged 31.
Following Glee, Michele has also starred in TV Series Scream Queens.
Watch: The first on-screen kiss between Rachel and Finn.