From the outside it looks like at least NFL 3 teams are trying to position themselves into moving to Los Angeles. That would be the San Diego Chargers, the Oakland Raiders and the St. Louis Rams. All three teams have histories in L.A. - the Chargers left L.A. in 1964 while both the Raiders and Rams left in 1995. And all three teams are currently involved in negotiations with their current cities over financing of new stadium deals.
Los Angeles is a desirable destination for NFL owners in many ways but most importantly it is simply a humongous market. L.A. County alone has 10.4 million residents. That is as many people as Buffalo, New Orleans, Jacksonville, Nashville, Charlotte, Indianapolis & Green Bay/Milwaukee combined.
In 1982 when the Al Davis owned Raiders moved from Oakland to Los Angeles they did it without league approval. The Raiders and the NFL were in court for over 11 years about Davis's unsanctioned move. Eventually the Raiders did receive about 20 million dollars in a settlement.
It is highly unlikely that any owner would risk a move to L.A. without the league's permission. When Davis did it in 1982 it was a big gamble. And by today's team valuations it would be a near ludicrous risk. The L.A. Clippers, Los Angeles 2nd basketball team, recently sold for 2 Billion dollars. An NFL team in Los Angeles would be at the very least worth as much as the Clippers.
Many NFL teams have used the threat of moving to Los Angeles as negotiating leverage when working with their current cities over stadium agreements. The Buccaneers, the Colts & the Vikings for just a few examples, all used Los Angeles as a bargaining chip in getting their new stadiums.
And that might be enough of a motivating force, that nine owners decide Los Angeles is more useful to themselves and to the league without a team than with a team and vote no to a Rams or Raiders or any other owners relocation dream.