The Scottish Sun says Hooper - who has 18 months of his current deal to run - had been in discussions with Hoops hierarchy.
Celtic gaffer Neil Lennon is still desperate to finalise a new deal.
Hooper underlined his importance as Celtic secured their first ever away win in the Champions League in Russia last week. He has been a prolific scorer since joining from Scunthorpe for £2.4million in 2010.
After watching him score Celtic's opener in last week's 3-2 win over Spartak Moscow, Lennon confessed: "We're hoping to talk to his agent soon about a new deal but he's just put £25,000 a week on his wage."