The 30-year-old Spaniard has been heavily linked with a return to his homeland, as the Reds continue to be linked with a number of replacement number ones.
Brendan Rodgers is believed to be considering a bid for young England stopper Jack Butland - a move that could pave the way for Reina to leave Anfield for the Vicente Calderon Stadium.
Birmingham City's precarious financial situation means that they could be forced to sell their prized asset in the January transfer window, with Liverpool reportedly leading a host of Premier League clubs that are fighting for Butland's signature.
Reina is likely to see out the remainder of 2012/13 on Merseyside, having been in impressive form of late, keeping three clean sheets in his last five Premier League games for Liverpool.
The Spain international has made a total of 379 appearances in the past eight years, since arriving at Anfield from Villarreal in 2005.
Now, according to Spanish paper AS, Los Rojiblancos boss Diego Simeone has turned his attention to Reina as the Liga club's other target, Osasuna goalkeeper Andres Fernandez, is being monitored by rivals Real Madrid and Barcelona.