The Leicester City forwards has been training with the Gers ahead of a move to Ibrox.
Rangers manager Mark Warburton has told reporters, via BT Sport, that he hopes the club can complete a deal for Leicester City striker Joe Dodoo but stressed that it is likely to be too late for him to take part in Tuesday night's cup clash.
Warburton has been very active in the transfer market already this summer but is hoping to make Dodoo his ninth signing of the window.
The 21-year-old striker has played just four senior games for the Foxes but has scored four goals in those appearances, with all four strikes coming in the space of two League Cup ties at the start of last season.
Dodoo has failed to break into the first-team picture at the King Power Stadium ahead of the likes of Jamie Vardy, Leonardo Ulloa and Shinji Okazaki, and with Ahmed Musa having been signed this summer, Leicester seem willing to sanction a move away.
Dodoo has been training with the Gers in recent days, but although Warburton appeared hopeful of a deal being completed, he admitted that the striker is highly unlikely to join in time to play a part against Annan Athletic on Tuesday night.
Warburton said, as quoted by BT Sport: "I'm hoping the paperwork is being finalised. The two clubs are talking. It's above my pay grade so I will let the clever people get on with that and I'll do my stuff out there.
"I think it will be too late for tomorrow night but fingers crossed we can get that one to completion. He has trained with us and he's a top young lad and a top young talent as well. I'll be excited to get him on board."
Attack is the one area of the pitch that Warburton is yet to strengthen this summer, and Dodoo would bring increased competition to a frontline which already includes the likes of Martyn Waghorn and veteran Kenny Miller.
After their opening 2-0 win over Motherwell on Saturday, Rangers take on Annan in their second Scottish League Cup group match tomorrow night.