Decide on methods when refactor classes to interface

So my question is:

When refactor existing class to an interface, how to decide if we need to move method to the interface or kept in class? will it depend on the goals of Unit test all the methods? or more like SOLID principles like Single responsibility or interface segregation?

• Assume all the methods in the class are public.
• Assume primary goal is better unit test abilities.

Thanks in advance for the responses.