"We would like to play Michigan and Michigan State again," Kelly said at a Notre Dame golf event in Olympia Fields, Ill.
Notre Dame is scheduled to host Michigan once more, on Sept. 6.
Michigan State, which had played the Irish every year since 1997, is off the schedule until the rivalry briefly resumes in 2016 and '17.
Michigan State athletic director Mark Hollis told the team's beat writers Wednesday that the schools tentatively have a home-and-home series set for 2026 and '27, as well as a neutral-site game, possibly in Chicago, in 2023.
But Notre Dame and Michigan -- annual opponents since 2002 and common opponents since 1978 -- have nothing set beyond this season.
"When [athletic director Jack Swarbrick] and I sit down and we start discussing 'what do you want to do?' we don't start or end that without having Michigan or Michigan State part of that conversation, and there's an SEC school involved in that conversation, as well," said Kelly, who sounded optimistic that Michigan would be open to future games. "I can assure you that Michigan, Michigan State and an SEC school is involved in those conversations. How that pans out, I'm telling you, it's a very complicated deal."
Notre Dame might be discussing the possibility of rekindling the Michigan series, but no overtures have been made to the Wolverines, Michigan athletic director Dave Brandon told ESPN.com via email Thursday.
"We have had no conversations with Notre Dame regarding scheduling since I was handed the letter on the sidelines, which formally ended the regular season games effective 2015 and beyond," Brandon wrote.
Notre Dame's new scheduling agreement with the ACC motivated its decision to suspend the Michigan series, which resulted in Wolverines coach Brady Hoke telling a crowd last May that Notre Dame was "chickening out."
Days later at the Big Ten athletic directors meeting, Brandon said the series would go on hiatus for a "considerable period of time," as no games could be scheduled until 2021 or '22.
Michigan's nonconference schedules are set through 2017, and a home-and-home series against Arkansas is on the books for 2018 and '19.
Kelly Wants ND To Keep Scheduling Michigan
Matt Fortuna discusses comments by Notre Dame coach Brian Kelly indicating a desire to keep Michigan and MSU on its schedule.