occupy somebody's thoughts
occupy somebody's mind

Here was something with which he could occupy his mind for some time to come.

That thought was one which had occupied his own mind.

I go to bed again, and begin trying to think of something to occupy my mind.

The ones who stood before him were enough to occupy his mind, and then some.

There's no question you've got to have something to occupy your mind.

After all, how much could the chief of police in this town have to occupy his mind?

The boy, however, had other things to occupy his mind during that spring and summer.

For the moment, however, something else was occupying his mind.

It was more for something to occupy his mind than with any real hope of making contact.

The thing that's occupying his mind just now is another matter.