The actress is said to be "heartbroken" after splitting from Romo on the eve of her 29th birthday earlier this month.
It has now been claimed that Simpson had been encouraging the American footballer to make a long-term commitment to her for months, leading to tension between the pair.
A source told Star magazine: "It got to the point where that's all she'd talk about. She would speak to him all the time about buying an engagement ring. Even in public.
"Jessica expected it last Christmas. Then she thought she would get one for New Year's Eve. And when by Valentine's Day it didn't happen, the tension between them became explosive.
"The night before her birthday, Tony warned her that he wasn't ready to buy a ring. They had a massive fight and Tony cut the cord for good."
Simpson has been linked to her ex-husband Nick Lachey since news of the break-up was announced.