Hamilton and her partner Colin Ratushniak were awarded three 9.5s for their performance on Sunday night, with Robin Cousins praising Hamilton for having "nailed every move".
"[She] improves every week," Gardiner told The Sun. "I feel what we are getting from this girl is very special: a lot of heart, a lot of spirit, beautiful placement and incredible partnership with Colin."
He added: "I wouldn't be surprised if we see our first 10 in the contest from Laura."
The judge also claimed that Sam Attwater should "worry" about his position as "frontrunner" in the competition.
"There have been inconsistencies in his routine but Laura has been more solid," he said.
Dancing On Ice continues on Sunday at 7.10pm on ITV1.