Kenneth has been without a club since leaving Dundee United at the end of last season and has trained with Airdrie in recent weeks.
McGhee told the Bristol Evening Post: "We've spoken to Garry and we're happy with everything that has been agreed and he'll join us subject to a satisfactory medical.
"I know what Garry is and if we can get him back to top fitness then he will be a very good signing for us.
"He's a traditional central defender and is everything we need at the back in this division and the one above."
- Dundee United