Jamieson, who lost his place to on-loan Rangers 20-year-old Liam Kelly, had been sent out on loan to junior outfit Bo'ness United earlier this month.
He would become Accies' third goalkeeping addition of the summer.
Gary Woods was signed permanently from Leyton Orient and Remi Matthews on loan from Norwich City.
The Premiership club lost Michael McGovern to Norwich this summer after his Euro 2016 displays for Northern Ireland.
Meanwhile, 16-year-old Jon McCracken followed him from New Douglas Park to Carrow Road earlier this month.
Jamieson had made 101 appearances for Livingston, 16 while they were in the Championship last season.
Goalkeeper Darren Jamieson has been released by Livingston, with the League One club saying that the 25-year-old is to join Hamilton Academical.