The teenage full-back`s stay at the Walkers Stadium is set to end in January.
Foxes boss Sven-Goran Eriksson told the Leicester Mercury: "Greg Cunningham, almost for sure, will stay for the rest of the season.
"I have spoken to Greg and spoken to (Manchester City manager) Roberto Mancini and both of them are happy.
"It is only a question between the clubs, but I can't foresee a problem. That will happen almost for sure."
Eriksson also revealed he was hopeful that another full-back, Kyle Naughton, would extend his loan spell from Tottenham until the end of the season.