The Premier League pair were both linked with the Turkish international over the summer, but neither club were able to lure him away from Madrid.
But, rumours suggest that the duo will form up their interest when the transfer window re-opens.
Both sides are believed to have scouts monitoring the 26-year-old, who has been in impressive form of late.
Turan is regarded as one of Atletico’s key men, and was a key part of the side that claimed the Copa del Rey and qualified for the Champions League last season.
It is believed that the midfielder has a release clause in his contract, although there is some debate regarding the figure needed to trigger it.
Arsene Wenger is believed to have significant financial backing for January, which could allow him to draft in Turan.
Liverpool boss Brendan Rodgers is in a similar position, and is thought to be keen to add to his side’s attacking capabilities.
Turan has previously indicated that he would be open to a Premier League move, highlighting Anfield as a desirable destination.
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