The Hardwicke Stakes at Royal Ascot is the next possible port of call for Defoe following his short-priced reverse at the Curragh on Sunday.
The Dalakhani colt won four races on the bounce last season, before failing to fire when well fancied for the St Leger at Doncaster.
He got his career back on track when making a successful start to the new campaign in last month’s John Porter at Newbury, however, and followed up in dominant style after being supplemented for the Jockey Club Stakes at Newmarket.
The four-year-old was a hot favourite to claim a first victory at Group One level in Sunday’s Tattersalls Gold Cup, but had to make do with minor honours in third behind the Aidan O’Brien-trained pair of Lancaster Bomber and Cliffs Of Moher.
Varian said: “He came home safe and sound and we live to fight another day.
“He wasn’t disgraced at all and I thought he ran a great race. He was coming back to a mile and a quarter on ground that was safe enough to run on but he would have preferred easier conditions, for sure.
“The five millimetres of rain they got on Saturday night made the decision (to run) that bit tougher. If they hadn’t got that I think it would have been a fairly straightforward decision to pull out, but we felt the ground was safe and the way the race was we felt we should give it a go.
“I don’t think he lost anything in defeat. He’s won a Group Three, a Group Two and finished third in a Group One so far season and I think his run on Sunday only enhanced his CV.”
Varian feels the combination of the shorter trip and drier ground meant Defoe was not seen to best effect on his Irish debut.
“It was frustrating as we got enough rain to run but not enough rain to see him at his best,” the trainer added.
“I don’t want to take anything away from the horse, we’re proud of him and I think the next time you see him he’ll be back over a mile and a half.
“The Hardwicke is a possibility for sure, but obviously it depends what ground we get at Royal Ascot.
“I think we’ll train him for that and go from there.”
Varian’s next potential Group One runner is Barsanti.
The six-year-old made a successful reappearance in the Buckhounds Stakes at Ascot earlier this month and could step up to the highest level in Friday’s Investec Coronation Cup.
Varian said: “We’re just going to wait before deciding whether to let him run. He wouldn’t want too much more rain.
“It looks like it’s going to be a small but select field.
“Hawkbill is a very good horse on his day and Cracksman is a champion.
“I don’t know if Idaho is turning up, but he’s pretty good as well, so it will be a tough race.”