Nearly 1,800 are employed at the Stafford Road plant
The manufacturer's American head was flying into the West Midlands on Wednesday to discuss the future of the plant.
The tyre manufacturer had warned in November that "severe over-capacity" in the industry threatened the truck tyre production jobs at its main UK plant.
But union leaders have said if the jobs go they may ask workers to vote on whether to take industrial action.
There are fears that if the 460 jobs go it could lead to the closure of the factory with the loss of almost 1,800 jobs.
Senior vice president of Goodyear, Vernon Dunckel, will meet with Transport and General Workers Union (T&G) national organiser Peter Booth and other representatives.
Mr Booth told BBC Radio WM that strike action was a last resort.
"Clearly if we are left with an uncertain position after today and tomorrow then our members are going to have a decision to make.
"Obviously we don't want to be entering into unnecessary industrial action.
"But at the end of the day while we still have a plant there and while we still have a workforce, that workforce is committed to fight to save its own future."
World leader
The Stafford Road plant in Wolverhampton has been producing tyres since the late 1920s.
In January last year the labour force rejected a deal under which 300 jobs would have gone in exchange for workers accepting a pay cut and longer hours.
About 1,800 workers are employed at the plant producing car, truck and agricultural tyres.
In 1999 Goodyear took a 10% stake in Sumitomo, surpassing its rivals Bridgestone and Michelin, to become the world's largest tyre manufacturer.