Kean has struggled with disciplinary issues in the past and his behaviour off the pitch has seen him attract criticism.
He joined Juventus on loan from Everton this summer and it has been claimed he had to give assurances to senior squad members that he would not step out of line.
Birindelli does not doubt the skills of the star forward, but is not sure he is completely committed to the Juventus cause.
The ex-Juventus player stressed that he would be delighted if Kean has returned to his boyhood club having become more mature, as he believes if that is the case the Turin club will become title contenders.
Speaking to Italian radio station Radio Bianconera, Birindelli said: “My doubts are not from a technical and tactical point of view, but about how much he wants to sacrifice himself and be part of this environment.
“If he’s back as a more mature player I’m happy because in that case Juventus will be competitive again this year.
“In order to maintain certain standards, the great champions must also be looking at something more, sharpening in the technical aspects.”
Juventus sporting director Federico Cherubini has insisted that he checked with Paris Saint-Germain before signing Kean and was told the striker’s behaviour was normal.