Both Scottish giants are in the market to make additions before the transfer window closes at the end of the month and they both want Cho.
He is available to move from South Korean side Jeonbuk Hyundai and will cost suitors around the £3m mark.
Celtic and Rangers are now going head to head to land the striker, who is keen to continue his career on British shores.
However, it is claimed that Rangers are currently working harder than Celtic to seal a deal for Cho.
Gers boss Michael Beale is keen to make a splash in the transfer window as he aims to inject fuel into his plans to drive the club forward.
He is holding talks with three players at the moment as he tries to add to the Ibrox group.
Rangers trail Celtic by nine points in the race for the Scottish Premiership title, but could score a clear blow on their rivals by beating them to Cho.
