I'm really sorry OP, but I don't think he actually wants kids, or rather, he only wants them if they're just a far off dream.
I note that you're not married either. Whose choice was that?
I'm not religious, nor do I think marriage would change my loyalty to a partner, but I do think that for many men, it's an indication that they're not fully invested in you. You might be lovely and make them quite content, but you're still not their 'The One'. Some men go one step further and buy a house and have kids with that woman, but they still won't marry their female partners because of this, and sometimes other reasons.
Sometimes those men future-fake or string the woman along for years until she's basically infertile or it's really too late for her to meet anyone else. The they leave her for a woman who is 10-15 years younger, whom they marry and have kids with in a space of a year or two.
I think if he really loved you, he would encourage you to split. If things don't work out for either of you in a few years time and you're both still single, then maybe you can get back together one day, but I think you should try to make the most of the fertile years you have left with someone who wants to have kids.
Go into it with open eyes though. At mid-30s, I'm guessing a lot of men who want to have children would look for someone younger. It allows more time for the relationship to develop naturally and takes a lot of pressure off.