The phrase "already being produced" is correct and usable in written English.
It can be used to indicate that something is currently in the process of being made or created.
Example: "The new model of the car is already being produced in the factory."
Alternatives: "currently in production" or "already in the making".
The chips are already being produced, he added, and the technology will be widely available to consumers in the second half of 2001.
We also plan to forge long-term collaborations with newspapers across the region so we tap into the best of the coverage already being produced.
The Merlin was already being produced under license in the United States by the Packard Motor Company, and by the summer of 1943 Packard Merlin-powered P-51s were coming off North American's assembly line.
Over at Grantland, Amos Barshad takes a stroll through this year's titles, and finds that several of them are already being produced, including the No. 1 choice, "The Imitation Game," a biopic about a World War II cryptographer.
Highlighting the scandal that half of the certified soy that is already being produced is failing to find buyers, WWF says there is little interest being shown by companies which tend to evade pressure from civil society.
The company has said its Model S and Model X electric cars are already being produced with the new system, which includes eight cameras, 12 updated sensors and radar with faster processing.
A second season has already been produced, and will be shown starting in late spring, said Jennifer Skorlich, a spokesperson for NBC.
For example, concrete can already be produced that actually captures and stores CO2 in the built environment.
Our schools are very good at selecting people who can come up with information that has already been produced.
A spokesman for the company that was awarded the original contract said much of the equipment had already been produced and was waiting to be shipped to Iraq.
