Asked what gave him that impression, Parker said: "He took a big gulp... I thought, 'mate, you're scared'.
"He should have fought me back then when I was 50 or 60 per cent [in May]. I'm 100 per cent now so he's in for it."
If more tickets are sold and more tune into the fight on the back of the tough talk then so much the better for all involved.
Asked about ticket sales, an issue thus far, Fury's promoter Mick Hennessy said he expected a crowd of about 8000. Earlier in the week he expected about 10,000.
Pressed on the lacklustre sales, he doubled down on his earlier assertion that Parker, 25, and Fury, 23, are at the start of their professional careers and are yet to make names for themselves, ignoring perhaps the fact that Parker is the WBO world champion with probably the quickest hands in the division and a genuine heavyweight force.
"That's the way boxing is now - there's so many events, the titles are splintered," Hennessy said by way of mitigation. "This is a great fight, I agree with you, it's better than other fights around at the moment but there are a lot of fights on sale and in the same area."
Both camps agree there will be no excuses should their fighter lose. Parker has come off one of his best ever camps and looks sharp in training - his movement, flow and timing perhaps at career-best level.
"The training camp is where you do all the hard work," Parker said "The fight is the reward and I'm looking to get my reward."
Fury has fully recovered from a debilitating skin condition which has put a handbrake on his career to this point, although, it must be said, he has never fought a boxer of Parker's quality.
Significantly, this fight will be one of the first events held at the Manchester Arena since the suicide bombing of Ariana Grande's concert in May which killed 22, including children.
Perhaps the most truthful and respectful line of all today at the home of Manchester United was delivered by Fury, who said quite unprompted about the prospect of fighting for the first time at the venue: "What's happened there, my heart goes out to all the families. No words can be said."
Parker v Fury at Manchester Arena will be shown in New Zealand live on Sky Arena from 8am on Sunday for $39.95.