Can you list a property for both sale and rent at the same time?

One of my tenants gave notice and will be out when the lease ends. I’m on the fence about whether to sell or just re-let. Ideally, I’d like to keep both options open. If a buyer shows up with a solid offer, I’ll sell, but if the right tenant comes along for a long-term lease, I’ll stick with renting.

But am I even allowed to market the place for both at once? And if so, does that mean paying double marketing costs? Or do most agents work it into one fee?