Since becoming the new boss of the Scottish giants, Steven Gerrard has been proactive in the market with seven players having already been signed by the Liverpool legend.
According to The Express, Gerrard is now looking to bring in Cooper, who has just enjoyed an impressive campaign with the Lions in the Championship.
Cooper is highly regarded at the London outfit and still has two years left on his contract, but it remains to be seen whether the 23-year-old would entertain a switch North of the border.
The player has spent his career in the South of England, with the left footer coming through the academy at Reading and representing the first team before eventually making the switch to Millwall.
Rangers could require a replacement for Bruno Alves, who is expected to join Italian side Parma.