The Rangers manager, Steven Gerrard, has made clear he wants Jake Cooper at Ibrox and is prepared to wait to land him, according to the Daily Express.
The newspaper claims Rangers tried to sign the Millwall defender in August, and made a series of bids that went as high as £3 million.
But while the London club were able to keep hold of Cooper then, it is suggested there is now concern they will lose the fight to keep him.
There is speculation, too, that the 23-year-old's contract contains a release clause that kicks into effect if Millwall - who are 23rd in the Championship - finish at the bottom end of England's second tier, which would appear to point towards a summer deal.
The Rangers chief scout, Andy Scoulding, is said to have filed a full report on Cooper after the Lions' 1-1 draw against Bolton last month, in which both he and another rumoured Ibrox target, Mark Beevers, were on target.
Rangers' centre-back pool currently comprises Connor Goldson, Nikola Katic, Gareth McAuley and Joe Worrall, although the latter pair are out of contract at the end of this season.
Cooper, who began his career at Reading, has impressed at both ends this campaign - scoring three goals and boasting the joint-most assists (6) of any Championship player.
Will Millwall lose Cooper to Rangers?
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