How to handle NC?

My ex and I broke up a month ago. During that first month we tried to be “friends”. Obviously that didn’t work. I constantly talked about getting back together and wanting him back and how things would be different. The past couple weeks I’ve tried to take a different approach and say I didn’t want to get back together right now, but maybe one day. He continues to tell me not to get my hopes up. He told me he doesn’t shut doors and he would never say never about us, but he doesn’t want me to wait for him. We were together 4.5 years and lived together. We broke up because the relationship got bad. Neither of us were happy and he says he fell out of love with me. He says he still has love for me and will always care about me, but it’s been a month and he’s already talking to this girl he used to hook up with before we met 4.5 years ago. He says they “click” and he feels like she could be the one. She lives 2,000 miles away and I don’t know if it’s just because he’s lonely and misses having someone show him attention or what.

My ex and I work together so I have to see him everyday. I decided to do no contact to see if there is the potential of us working things out. I honestly think things could be amazing now that we’ve talked and no what went wrong. I know that I need time to be single and change things and I have a lot to work on but I do still want him back eventually. I’m on day 2 of no contact. This is after the month of us trying to be friends and failing. He’s texted me a few times asking me questions and he talks to me at work. I stayed home sick today and he texted me asking if I was coming in. Then later he asked if I was feeling better and tried to start a conversation. I didn’t tell him I was going to stop talking to him and I feel rude just randomly stopping contact and ignoring him so I’m not sure how to handle it. I’ve waited before answering and been very short with my answers. I don’t ask him anything or pursue conversation. I don’t want him to get mad at me and think I’m being rude. What do I do in this situation? I want him back. And I honestly don’t know what to think about him and this girl. I want to hope it’s a rebound, but he says things about her that he never said about me. Is he just trying to make me jealous? He doesn’t ever offer the information, I was asking him before I decided to do no contact. I just don’t know what to think or how to feel. I honestly do believe things could be better if we had some space.