The Portuguese worldwide is believed to be angered by the new offer from Madrid.
Reports have been gathering pace lately that La Liga and Champions League holders Madrid want to replace Karim Benzema at the end of the current season, and have their sights set on the 24-year-old striker.
Real Madrid were determined to extend his stay beyond 2021, despite the player not being interested in a new deal.
Ronaldo posted a photo Sunday on Twitter of him with the baby's mother, Georgina Rodriguez, and his oldest son in a hospital in Madrid.
Ronaldo is angry with Madrid's new proposal and is reportedly ready to leave for a cut-price fee which would be reasonable for Madrid.
And according to Spanish transfer outlet Don Balon, numerous Real players are fed up with the Portugal global.
Meanwhile, Spanish football journalist Edu Aguirre who works for Spanish TV station El Chiringuito reports that Ronaldo has informed club president Florentino Perez of his decision. "I'm very happy with the contract I have".
The Portugal worldwide has undergone a dip in form in recent months, scoring just one La Liga goal so far this season.
With Alana Martina's birth, Ronaldo has officially become a father of four.