Is it possible to patch a class instance with an existing Singleton instance?

I have a class representing our DB layer which is being instantiated internally in some classes (I cannot pass it as an outside parameter)

For example:

class MyClass(object):
    def __init__(self):
        self.dbapi = DatabaseAPI()
        self.timeout = 120

    def some_methods(self):
        pass

We're writing some Unit tests, and we'd like to mock the self.dbapi with an existing instance which we'll be creating before the test runs.

for example:

my_dbapi = DatabaseAPIMock()
...
...
@patch('MyModule.DatabaseAPI', my_dbapi)
def my_test(self):
    my_class = MyClass() #<---This is where I'm not able to mock the DatabaseAPI

This is what I tried to achieve so far, but from debugging the code I see that the self.dbapi is instantiated with the real object and not with the pre-made mock.

What am I missing?

BTW, we're running python 2.7

Thanks in advance!