The Lanarkshire side are said to be locked in talks with the former Hibs coach about replacing Martin Canning and hope to have a deal concluded before their clash with Dundee this weekend.
Canning was axed by Accies on Tuesday morning after a run of eight defeatsw in their last nine games.
Rice has a wealth of coaching experience though this would be his first venture into management.
The 55-year-old previously worked under Ian McCall at Greenock Morton, Airdrieonians and Falkirk.
After McCall left, Rice remained to work under John Hughes, who he followed to Hibs and Inverness CT.
He left Inverness this past summer to work alongside Alan Stubbs at St Mirren and remained there after the manager’s sacking.