The report claims terms have been agreed with the 23-year-old lock forward but an official announcement has been delayed along with other signings by Edinburgh such as that of Marshall Sykes.
Davidson joined the Warriors at the start of last season, having previously been on a short-term loan at Scotstoun from Newcastle Falcons. Originally a Glasgow Hawks player before turning pro, he has been capped by Scotland at age-grade level, but only made a handful of appearances for Glasgow this season.
New Glasgow head coach Danny Wilson is expected to announce a number of new arrivals over the coming weeks.