He did tell me her name and that she had given him a ride home sometime ago.They exchanged phone number. She has called him on several occasions and left voice messages.
He has returned her call. The reason I know this is because I can check his cell phone log and track all our calls. He stated to me that he showed her a picture of me. So this co-worker knows he is married. He has called her cell number and I can see that it has been very brief conversations l min or 10 minutes. I just feel he is being secreative at times about talking to her. They do not speak on a daily basis. I has always said to me that he has had female friends and that all they are. She I confront me with this or just leave it alone and monitor the situation.

I would be inclined to treat it the same as if he were getting calls from male co-workers or female relatives. Some interest ("What did X want to talk to you about today? Does she need a lift?") but not obsession.

The fact that he's told you about her, and shown her your photo are good signs that he's not sneaking about.

Take his word for things, but why not meet her for yourself. She sounds like a co worker, and friend, so ask him casually if she can meet you. Then you can put suspicion to bed.

Put a stop to it now. The same happened to me. In my case she was married herself and we know each other. It didn't matter. They ended up having physical affair.