Rumours of a move have been circulating since last year and a BBC report claims the Stormers player will follow friend and club-mate, Scotland centre Huw Jones, in moving to Scotstoun next season, after his commitments in South Africa.
It is thought Kebble is considered a project player by Scottish Rugby, who have monitored him for several years.
As he is not tied to South Africa, the prop could become eligible to represent Scotland after three years' residency.
Kebble, the son of ex-Springbok prop Guy Kebble, who won four caps from 1993-94, won the 2012 Junior World Championship with South Africa U20s.
The 124kg (19st 7lb) prop is chiefly a loose-head, but can play on either side of the scrum.
He has made 34 appearances for the Stormers in Super Rugby and helped Western Province to the 2014 Currie Cup title.