Steven Gerrard tried to sign the 23-year old in August and made a series of bids, going up as high as £3million.
Millwall refused to sell but he remains firmly on the Ibrox radar.
Chief scout Andy Scoulding travelled to the New Den to watch Cooper net a late equaliser for the Lions against Bolton at the end of last month, and filed a full report for Gerrard.
It’s understood Millwall are concerned they could end up losing the fight to keep their prize asset.
It has been suggested that Cooper has a release clause in his contract if they are relegated or finish at the bottom end of the Championship.
As it stands they are third bottom on goal difference.
Gerrard has made it clear he wants Cooper and is prepared to wait. If any deal is to be done it is more likely to be in the summer, although Millwall might consider selling in January.
The match against Bolton also allowed Scoulding to run the rule over Bolton defender Mark Beevers.
He is another player Rangers have looked at to fill the left-sided central defensive role. The 29-year-old, who also scored in the game, is out of contract in the summer.
Rangers’s main priority in January is another striker with Liverpool’s Dominic Solanke high on the radar.