The young defender has been a target of the Glasgow-based team for some time now, with Steven Gerrard looking to move quickly in this transfer market to revitalise his squad.
9 new players have already come in to Ibrox so far this summer, including Jon Flanagan and Connor Goldson in the defensive line, but the former Liverpool captain wants to further strengthen that area of the pitch.
According to 'Sky Sports', a bid has been made by the Scottish team, but Millwall are keen on keeping the player at the Den and will remain resolute in that aim.
Cooper joined the club from fellow Champiosnhip side Reading only last season, and made 35 appearances in the league to help his side achieve a 8th placed finish.
Meanwhile, Steven Gerrard and his team are hoping to challenge city-rivals Celtic for the Scottish Premiership as they hope to stop Brendan Rogers's men from winning their eighth-consecutive league title.