Verizon Communications Inc. is proposing to shake up the pay-television business based on a simple premise: it wants to tie the fees it pays to carry TV channels to how many people actually watch them.

Verizon, whose FiOS TV is the nation's sixth-biggest pay-TV provider, with 4.7 million subscribers, has begun talks with several "midtier and smaller" media companies about paying for their channels based on audience size, according to Terry Denson, the phone company's chief programming negotiator. He declined to...