There are four employees in the team that reports to me, and they're very close with one another. They go to lunch together every day. I'm glad for the camaraderie among the four of them, but it would be better for their career development and their relationships inside the company for them to reach out to employees in other departments. At times, the cliquish nature of their friendship reminds me of high school. But I don't know that I would feel comfortable advising my employees on how to create relationships inside the company. I would appreciate your advice on this issue.
Rest assured, your employees' professional relationships are a very appropriate topic for you (as their manager) to address. But you're right in not wanting to position the advice as an admonishment. You want to suggest ways in which your team of direct reports can broaden their relationships inside the company, but you don't want to a) rebuke them for having had so many lunches together, or b) tell them with whom they need to have lunch in the future.
So your message might go like this. "Look, team, let's talk about our relationships inside the company. Are those important to us? How so? How could we make them stronger? Do we, for instance, feel that we know the critical players in other departments as well as we would like to? I wonder whether we could try the approach of picking some key people to get to know better, and seeing how doing that might influence our success."
If you want to, you could offer to fund one restaurant lunch per employee on your team, once a month for a quarter—so that you're turning the meet-some-new-people advice into a true work assignment (much like taking a customer or vendor to lunch), while not expecting your team members to foot the bill for all those lunches.
If you do this for three months, your team of four should have had three networking lunches apiece for a total of 12 new contacts inside the company. Your guys will get practice making conversation with someone other than their own three best workmates, to boot—for a cost of about $240 (at $20 per lunch for two—I'm thinking the corner deli rather than a white-tablecloth restaurant). Would that be a worthwhile expenditure to cultivate new and fruitful relationships across the organization, and to give your team members some practice in internal networking? It might be.
If that's too elaborate, why not buy sandwiches and invite one department per quarter to have lunch with your team? There are a number of ways—short of assigning lunch partners or forbidding your direct reports from bunching together as a pack—to make the point that spreading their wings, network-wise, would be a worthwhile endeavor.