convolute pre-trained network over a bigger image with keras/tensorflow

Question

I want to define a tensorflow convolutional model by including a pretrained model inside it.

I have a pretreained sequential model defined as:

kernel_size = 11

def my_base_model():
    model = keras.Sequential([
        layers.Flatten(input_shape=[kernel_size, kernel_size])
        layers.Dense(32, activation='relu', name="layer1"),
        layers.Dense(1, name="layer2", activation="sigmoid")
    ])
    # ...
    return model

model = my_base_model()
model.fit(...)

Now, I want to use this network as a filter for slide arbitrary-size images:

I order to make it easier/streamline, I think in building another CNN network. For example, supposing the input image shape is (640, 640). In order to achieve a (640 - 11 + 1, 640 - 11 + 1)` output image:

def my_cnn_model():
    model = keras.Sequential([
        layers.Conv2D(1, (kernel_size, kernel_size), activation='linear', input_shape=(640, 640, 1)),
        # <== including base model here
    ])

    return model

Obviously, I cannot just append my_base_model there because I want to apply the model for each 11x11 square.

Is it possible? If not, is there another way to implement it instead of directly sliding the 640x640 with 2 nested for loops?