The Iceland international has fallen out of favour under Brendan Rodgers and is believed to be keen to move on from the Madejski Stadium in a bid to find regular first team football.
The players agent, Olafur Gardarsson, admits there is interest from a number of clubs whilst confirming the 34-year old was keen to find a new club.
"We will see if we can find a move for Brynjar in January," Gardarsson told skysports.com.
"He is used to playing regularly, but has only played in half the games this season.
"When a new manager comes in he has new ideas and Brynjar understands this.
"There is interest in Brynjar from England and Scandinavia, but he would prefer to stay in England and we will see what happens in January."