is it possible for an interface to have an already instanced object as an attribute?

I am creating an interface with many implementing classes and there is an attribute they must all have;
I guess it's better to put that attribute in their interface than writing many constructor lines, but attributes can only be static final and require to be immediately initialized.

public interface Interface{

     static final AttrType attribute = new AttrType( *something* ); 

I have 2 problems: this attribute is a class and its constructor needs some other type parameters not just ints, and also it shouldn't be initialized here, I need all implementing classes of the interface to work on the same instance of AttrType which as i said I won't instantiate in the interface.

So, as I am not expert enough, is there a way to do this in the interface or I should just write a line in every subclass' constructor to put in the one AttrType instance they need?

Would it be possible to add also a common base class to go with your common interface which all the classes could inherit? Then the common base class constructor could contain the attribute instance. Also you could consider using an abstract class instead of interface.

Java interfaces describe what a class can do, rather than what a class is. Therefore, an interface only describes methods.

You could handle this in a few ways:

Using an interface, you could have a getter for the variable, which would force the implementing classes to have the variable. Something like "public AttrType getAttribute();"

Or you could create a class, probably abstract, which implements the interface and has the variable, and its getter and setter. The subclasses all would inherit this variable and behavior.