The 23-year-old's deal is due to expire at the end of the season but Christie, who joined from Inverness in 2015, does not expect there to be any complications in negotiations.
Christie, who has had two loan spells at Aberdeen, has scored in each of his last three games and has earned praise from Brendan Rodgers for his performances.
"I love being a Celtic player and want to extend my stay here. It is looking positive and hopefully me and the club can come to an agreement quite soon," Christie said.
"With the contract talks, I had to talk to the manager and he was brilliant and he let me know he saw a future here at Celtic which is all I needed to know.
"That's all I needed to know and with that knowledge I can hopefully kick on.
"It's up to me to kick on but I feel like I am a part of this squad now and can have a big impact between now and the end of the season."
Celtic's next game comes against RB Leipzig at Parkhead on Thursday.