The spinner endured a troublesome summer on a personal level, making headlines for off-field issues including urinating on a bouncer in Brighton.
"We have got to make sure we look after him off the field," Cook told reporters. "Sometimes you take a second spinner on tour and you know you might not play games. It can be very hard to carry the drinks at certain times. We need to get Monty in the right frame of mind so if he's called upon.
"We have to be aware that sometimes he struggles with long tours - that is fairly common knowledge - and we look after him. That is one of the responsibilities we have as a leadership group. Clearly he had a tough summer, and probably tough year or so.
"A lot of us didn't quite know what he was going through off the field if we are being totally honest and it all came to light with a couple of instances in the summer. But I certainly think he's on the right path now."
The first Ashes Test will get underway at the Gabba in Brisbane in November.