The 21-year-old is out of contract at the King Power Stadium and has been training with Rangers this week, although because the Foxes offered him a new contract they are owed compensation for the youngster.
Warburton is hopeful of getting the final paperwork completed by early next week, though, as he looks to add a ninth new signing to his squad this summer.
"We are trying to get things to completion. There is paperwork between the clubs. If all goes well, we can work with him early next week, but as yet it's not finalised," he told reporters.
"I see him as a young, exciting striker, I see him probably more central than wide, but we like players with that flexibility of offering us width. If we have players with flexibility of position, then it gives us far more options.
"We have to add value and quality to the squad, and add characters who add something off the pitch as well. He came in and trained with us, fitted in really well. He was chatting away to Joey Barton, to Lee Wallace, the skipper, and Kenny Miller, and the young guys as well."
Dodoo made just one Premier League appearance for Leicester on their way to the title last season, but did memorably score a hat-trick in a League Cup match against Bury before later joining the League One side on loan.