Riise left the Reds and joined Roma in a £5million deal in 2008, but he is now keen on a return to Anfield.
The Norwegian defender is hoping to be included in a swap deal involving his replacement Andrea Dossena.
Dossena have been a disaster since joining Liverpool in a £7million move for Udinese and could be set for a return to Italy in January, says News of the World.
