There's no evidence it was even considered.
I think uniting the monarchies ran far more to Henry VIII's tastes when it was the future Edward VI who was to be the groom. He wasn't quite as forward-thinking as his father in imagining that a united Britain would inevitably be anglo-centric, and that that was what mattered. Instead, preserving a male line of Tudors and giving them the biggest realm possible was his preoccupation.