The 14-goal striker has 18 months remaining on his current contract with the Parkhead club holding a further year's option.
However, Hooper, who turns 24 next month, has given a clear message to Hoops chief executive Peter Lawwell and manager Neil Lennon that he wants to discuss a longer deal.
Hooper told a number of newspapers: "I would be keen to talk.
"I'm just here to score goals and to win games. But I would be happy to stay and sign a contract. I couldn't be happier in Glasgow."
Hooper, a £2.4million buy from Scunthorpe in the summer of 2010, scored 22 goals last season and netted in Thursday night's 1-1 Europa League draw against Udinese in Italy, albeit it was not enough to keep the Parkhead club in the competition.
"I feel I've improved as a player at Celtic because I am more of the type to get on the ball now and create things, as well as scoring as many as I can," he said.
"I'm still learning things every day from the people here.
"I didn't know if I'd settle in so quickly, but I also didn't realise just how big Celtic was until I got here.
"I settled in well by scoring a few early goals and the supporters have helped because they have been great with me. It's going well."