This will not happen any time soon. The reason it is not happening any time soon is that there currently no NFL stadium in Los Angeles, and those things take a while to build. Seriously, it's taken roughly a year for them to put a small cafe and an exercise room in at the office part where I work; and whether or not you include water fountains it's my understanding that stadiums take considerably more work.
There will be a football stadium in Los Angeles that whatever team moves there can use to siphon ungodly amounts of taxpayer money.
This will not happen any time soon. The reason it is not happening any time soon is that, besides the difficulty of acquiring the prerequisites for building a giant stadium with associated parking lots in LA, the NFL is not going to green light this until the teams that are not moving to Los Angeles have successfully leveraged the threat of moving to Los Angeles into massive stadium boondoggles of their own. Only once that is done, and the last bit of municipal money that is not from LA has been squeezed out of whatever chunk of flyover country the teams that are not moving to LA are from, will they break ground on the new LA stadium.
It is, when you look at it, quite elegant, a streamlined machine for turning tax dollars into stadiums and coincidentally relocating one team - my guess is the Chargers - to the City of Angels.
And when it is done, and the last dollar pulled out and the last press conference held to talk about how excited Drew Brees is to be playing in LA now, then the league will look at newly vacated San Diego, or San Antonio, or Oklahoma City, or London (Here's a secret - it takes a much smaller city to support an NFL team than any other major sport. You only need to fill up the stadium 10-11 times a year, as opposed to 81+ times for baseball) and do it all over again.