occupy somebody's thoughts
occupy somebody's mind

And right now there are other issues occupying our thoughts.

In truth, she'd had other things to occupy her thoughts.

He had other, more important matters to occupy his thoughts.

They might be a little bit, but it's not what occupies their thoughts.

He had occupied her thoughts since the first time she'd laid eyes on him.

The history of our efforts at space travel is not something that has ever occupied my thoughts!

No one woman had ever occupied his thoughts so completely.

During the next few months I did write something which occupied my thoughts for a while, more or less.

Especially things that have occupied your thoughts for a long time and about which you care a lot.

When she looked at the picture, it always occupied all her thoughts.