So I guess it depends on what you mean when you say you'd like to "cultivate" this new friendship on your own. By doing what? Sending text messages to each other? Going to hockey games? Playing tennis?
The truth is, marriage shouldn't mean the end of friendships, and many marriages suffer when they become too insular. It's possible your husband is insecure and paranoid, and if so, you might want to reassure him of your love. Tell him, "Luke is no threat. He just happens to share my passion for tennis (or whatever), which you don't, so who cares if we play sometimes?"
But if you want your marriage to last, make sure your shared passion remains on the court.