I have a custom framework where i have a class/method which uses my own Cache
class.
Currently it is tightly coupled. So a method instantiates the
As per OP request
Especially since it will be part of the framework, you should inject the Cache. A DI Container is the best solution here, you can config the actually Cache implementation as a singleton. Your proposed solution is tightly coupled to some service and hard to test in isolation. Actually it looks more of a service locator pattern rather than provider.
If you're using a Factory that won't replace the DI Container. THe point of DI is that the code shouldn't be coupled to an outside static service. Unless you have a very good reason, any object should use only the injected (via constructor or as method argument) dependencies.