The club are considering a tour of the Far East, where their popularity has grown since the signings of Shunsuke Nakamura and Mizuno.
However, SPL leaders Rangers face a possible fixture pile-up if they continue to progress in the Uefa Cup.
Putting back the final day of the Premier League season - currently scheduled for 18 May - could allow them some breathing space.
A spokesperson for the club said: "Celtic have been considering a possible invitation to tour Japan and this will be looked at in further detail over the next few weeks, but no final decision has yet been taken.
"Clearly, with Celtic now enjoying great support in Japan, this is something which the club needs to consider, as it did previously when we made a similar visit.
"The club can state very clearly that any discussions with regards to an end-of-season tour have been continuing for some time and have absolutely nothing to do with any recent debate around extending the SPL season."
Mizuno featured in reserve wins over Rangers and Gretna, although he had to be withdrawn with an ankle knock in the second game.
"I felt comfortable playing in the game and I was happy, as well as relieved that I'd managed to play my first game in Scotland," he said.
"It is a bit more physical. You find the players are that bit taller and sometimes you get challenges when you don't expect it."