I wonder if he will reach out to me after more time has passed and when he feels ready for a serious relationship.

I have had people I dated when recently divorced circle back & ask for a second chance, but it has never been because they were ready for a serious relationship. It was the garden variety “circle back to an ex when you’re lonely”

He also mentioned that he wants to be friends, which I am not sure about. Do you think keeping in touch will make it more likely for him to consider a relationship with me in the future when he feels ready?

No one can say for sure, but sticking around to be friends with someone you want a serious relationship for is a recipe for disaster. He’s going to be dating other people. It can take a toll on your self esteem to be on someone’s backburner & there will be temptation for your to want to “prove” yourself by doing girlfriend things and hooking up & get hurt.