The X Factor was launched in 2004 but has been off air since 2018.
ITV aired a celebrity version in 2019 which was won by reality star Megan McKenna.
During a panel at the virtual Edinburgh TV Festival, Lygo was asked if the show will definitely return next year, and what format changes are planned.
He said: “It’s not definitely returning, it might return.
OHHHHH MYYYYY GODDDDD my dream has come true I’ve worked my whole life for this moment thank you so much to everybody who voted words cannot explain how I feel right now I cannot believe I have won @thexfactor !!!!!!!!! pic.twitter.com/tlFDdclhUQ
Advertisement— Megan McKenna (@Megan_Mckenna_) December 1, 2019
“It was our most successful entertainment show for the best part of a decade and you need to be wary of changes, we all think there were too many changes towards the end of the run.
“I’m sure X Factor will be back at some stage, it’s really when is the right moment.
“Simon (Cowell) controls it, when does he want it to come back? How does he want it to come back? And hopefully we can be a part of it.”
Cowell bought Sony Music Entertainment’s stake in The X Factor earlier this year, as well as Britain’s Got Talent.
He also gained ownership of all the international versions of both programmes.
At the end of 2019, Cowell signed a new five-year deal with ITV which will see his shows appear exclusively on the channel until at least 2024.
It includes five series of Britain’s Got Talent and at least one of The X Factor.
Lygo also discussed the future of another of ITV’s flagship shows, I’m A Celebrity … Get Me Out Of Here!.
Our first Meet the Controller of the day is Kevin Lygo, director of television @itv. Tune in at 13:10 as Lygo delves into what to expect from the country’s largest commercial broadcaster throughout the remainder of the year and for 2021. Sponsored by @freeviewtv #EdTVFest pic.twitter.com/7bGe97m7yG
— Edinburgh TV Festival (@EdinburghTVFest) August 27, 2020
The programme will relocate to the UK from Australia for the forthcoming series and will be filmed at Gwrych Castle in Abergele, North Wales.
Lygo said: “I certainly didn’t want a year without I’m A Celebrity, it’s a premier, wonderful thing that has done so well.
“Australia was always going to be a challenge because of travel, so we started planning early on for what happens if we can’t go.
“The first aim was to get to Australia but when it became clear we weren’t going to make it, we were scouring the country for suitable locations.
“We found an extraordinary place, a beautiful Walt Disney castle, crumbling, tough and we just thought this looks like the place.
“I think it will be fascinating to see what audiences do and to come up with different challenges and tasks, the team I know are stimulated by this and thrilled about it.
“We had booked most of our celebs, we were worried they thought they were going to hot, sunny, bug-infested Australia and now they are going to north Wales in the dark, but everyone is still there and excited.
ITV today announces that the 20th series of I’m A Celebrity...Get Me Out of Here! will be filmed at the historic Gwrych Castle, Abergele in North Wales. https://t.co/uevRHrW0CV pic.twitter.com/ElebFTaUNn
— ITV Press Centre (@itvpresscentre) August 27, 2020
“I think it will be fascinating to see and have this reboot of a treasured brand forced upon us, I think is a good thing.”
Lygo added he is “assuming” Love Island will be back next year after the summer series was scrapped due to coronavirus.
He said: “It’s a really important show and a wonderful show. I think we took the decision with a heavy heart to cancel the winter series. In the summer, look, it’s a long way away and so we hope we’ll be there (in Spain).
“They are shooting it now in America, they’re doing it in Las Vegas… there are ways, you know, you isolate people beforehand, so at this stage it is still a long way away and we will proceed along the basis that we are going to do it.
“If we don’t do it in Majorca, maybe we’ll have to think like I’m A Celebrity, we’ll find a new place to do it or something. We need it and we are assuming it will return.”