You don't mention how long you have been a widow, he may be afraid it is too early for you to want to date.
To me he sounds shy, so if you like him, why don't you ask him for a cup of coffee after work, or invite him to something where there are lots of people around, an opening of a new exhibition at a museum or art gallery for instance.
If you don't like him, or feel he is stalking you, nip this in the bud, NOW. Have a quiet word with your boss at work, asking him or her to call this man to heel when he hangs around your desk instead of doing his own work. Say that his attentions are making you uncomfortable.
What exactly has he found out about you? If it is only things he could have found out by asking around the office, or reading your Facebook or LinkedIn profiles, if you have them, then there is nothing to worry about.
If you like him, use the fact that he knows a lot about you, say, "You seem to know a lot about me, let's have a cup of coffee after work, so you can tell me all about you"
By unmarried, do you mean he never has been married, or is divorced? At our time of life, it might just be as well to steer clear of a man who has never married, if you want to re-marry, that is, as he probably is not interested in marriage.