The three-year-old colt is priced at 5-2 to land the world's oldest classic, which will be contested by a field of 14 runners.
With good ground expected this weekend, Newmarket-based trainer Varian is hopeful that he can be in the winners' enclosure following the famous race.
"The rain they had at Doncaster on Saturday was very useful for us," Varian told The Times.
"There is very little chance of any more this week, but this is September, not July. Tracks don't get baked by hot sun at this time of year, so we should not have the same problems."
Kingston Hill finished second in the Epsom Derby in June, but was withdrawn from the Great Voltigeur Stakes at York due to the fast ground.
Varian revealed that a tilt at the Prix de l'Arc de Triomphe at Longchamp on October 5 is also a possibility.
"It's no concern to me that he hasn't run for a while and I'd be keen on the Arc if all goes well at Doncaster," he said.
"I know it's never been done, winning the Leger and the Arc in the same season, but he hasn't had a busy summer and Andrea [Kingston Hill's jockey Atzeni] got off him the other day and said he'd never felt better.
"First things first, he has to win at Doncaster, but he has an amazing constitution and could go on to a target three weeks later."
Atzeni is confident his mount will make the one-mile, six-furlong trip and pull off another victory at the Yorkshire course - where he won the Racing Post Trophy last year.
"He ran a great race in the Derby and the way he stayed on up the hill over what I would say is a stiff mile and a half at Epsom suggests there is every chance he'll stay [the distance]," he told At The Races.
"The way he travels, the way he settles, I think the trip won't be a problem."
The Michael Stoute-trained Snow Sky, and Romsdal, trained by John Gosden, are also expected to be in the St Leger shake-up.
Stoute has another contender in the form of Kings Fete, but jockey James Doyle is likely to side with Snow Sky.
Aidan O'Brien was able to celebrate his fourth St Leger winner when Leading Light passed the post first last year and the Irish trainer revealed he is only likely to enter Granddukeoftuscany, with Kingfisher sent to Leopardstown instead.
Windshear, trained by Richard Hannon and ridden by Richard Hughes, is another contender for the £650,000 prize money in the eagerly awaited race on the final day of the four-day meeting.