Is this man attracted to me, and if so, what steps should I take to follow up?

It sounds like he may be interested, at least in getting to know you better. If you feel the same, why not ask him out to lunch?

I second what @augustlan said at very least take him up on his offer for a ride and ask if you can repay his kindness by buying him a cup of coffee or drink after work on the way home. Go to a place where you can talk outside of work and you should be able to tell better if there is sincere interest there for more.

Contact him and suggest meeting somewhere in the neighborhood for coffee.

Since you’ve chosen the username “Hopeless Romantic”, my suggestions will actually be a bit more cautious than those above. I am inferring by that choice of username that you are longing to find a romantic partner – and there is nothing wrong with that. However, sometimes that yearning can lead us to act impulsively and move hastily. I have learned from experience that if a true compatibility exists, it will be all the better for having taken one’s time to get to know one another and to be friends before allowing a romance to blossom.

Proceeding cautiously is especially important, since you do work for the same employer – no matter how large or how separate your departments may seem, if things don’t go well, it could have professional implications, as well as personal heartbreak.

I would suggest striking up a casual friendship with him – carpooling might be a good way to start out, because then you’ll have plenty of time for conversation and to really get to know if there is strong relationship potential. I just mentioned in another comment how much we learn about a person from observing the way they interact with others (e.g. gas station attendants, drive-through cashiers) and how they handle life’s inevitable frustrations (e.g. traffic jams). You’d even get a sense of their world views in how they respond to news stories, and find out if you have similar cultural interests in what you choose to listen to – music, audiobooks, news radio, talk radio, etc.

Even if there is a chemistry there, it’s OK to say that you want to move slowly if your goal is to build a serious, committed relationship. If his intentions are the same, he will not only understand, but agree. Don’t let your romantic dreams keep you from using your intellect. Finding the right life partner is not just about romance. Good luck!

He may be interested but he also might have just wanted to be nice. It is hard to tell. However, good job at declining his offer since you don’t know him. You shouldn’t get into a car with someone you don’t know. Next time you see him, definitely greet him and let him do the rest. When a man wants to take you out or get to know you it will be obvious. Oftentimes, we make things so much more complicated than they are. Men, in particular, are not hard to figure out as they go with how they feel. Give him a second chance to come up to you and take it from there.