AMD is not only in charge of producing GPU and CPU for both Xbox and PlayStation, the company has also got its hands full with manufacturing its own GPU. Xbox head Phil Spencer also said he got on the phone with AMD CEO Lisa recently with regards to the matter.
In this case, Microsoft is not alone. The same problem of supply shortage also happens to Sony too, since the PS5 uses a similar chip as the Xbox Series X does. The supply issue could also last until at least April. Shortage of the chip supply is not the only problem that the consoles are facing. Another problem is the issue of scalpers who used the bots to buy the consoles. Later they would resell them to make a profit. (Source: Gizmodo, VGC)