Shunsuke Nakamura has been out since October with a knee injury and the timing of his return to action coincides with the imminent signing of the 22-year-old JEF United midfielder who has been granted a work permit.
Strachan said: "I don't think there is any real stumbling block (with Mizuno).
"We have a work permit and he wants to be here.
"I think it's a case of tying it up. His contract finishes at the end of January so I think Peter (Lawwell, Celtic's chief executive) is tying up the loose ends with his club.
"He (Koki) is just a pure footballer.
"Naka added a physical presence to his game when he came here and when you add that to his skill, you have Scotland's player of the year last year.
"We have missed him for the last two or three months but he is coming back now and if he (Koki) is half as good as Naka then we will have another cracking player."