According to Scotland Rugby News, the former Edinburgh captain Grant is understood to be among those in consideration to replace Peter Murchie as defence coach.
Glasgow have been interviewing for a replacement for Murchie who departs for Japan at the end of the season.
Grant, born in Botswana to Scottish parents, played 138 times for Edinburgh before taking on a coaching role at the club under Richard Cockerill.
Grant also assisted Cockerill with the Georgian national team, helping them to the Rugby Europe Cup 2025, and spent five years on the Ulster coaching staff before leaving last summer.