The 20-year old winger has been watched by Spurs in the weekend's draw with Hibernian with reports suggesting the North London were set to come in with an offer in January.
Redknapp has confirmed interest in the Scotland international but said at the moment it has gone no further than simply monitoring his progress.
"We've had good reports of what is obviously a good player. But he belongs to Celtic and that's as far as it's gone," Redknapp said.
"We haven't gone any further.
"If we were to go any further, then I would phone Neil Lennon and have a chat with him about the boy."