Torrance Mayor Frank Scotto told Eyewitness News that city leaders contacted Toyota immediately after hearing the rumors last week, but have not been able to confirm the reports.
Scotto said Torrance has repeatedly tried to keep Toyota, but says they have now run out of tools at the city level.
Torrance officials said they would be "extremely disappointed" if Toyota were to relocate.
"Worst case scenario they close down the facility, 5,000 employees, 5,000 jobs in California, 5,000 mortgages, 5,000 grocery bills," said Councilman Bill Sutherland.
According to the Dallas Morning News, Toyota is about to lease a massive facility in Plano, Texas, that could house 4,000 workers.
In February, Texas Gov. Rick Perry launched a campaign to lure California businesses away with what he calls low taxes and sensible regulations.
Sutherland is hoping Toyota's announcement will be much like Honda's recent move in which only a couple dozen jobs were relocated. He says the city will fight a major move.
"If there's anything we can do to prevent it, we will do it, and I would like to hope that if there is anything the state can do to prevent it, the state will do it," he said.