The 50-year-old took to the social networking site to show his displeasure at Los Blancos' 3-2 victory over Manchester City in the Champions League, calling Mourinho a "psychopath" a number of times during his public attack on the Portuguese manager.
| REAL MADRID LATEST
|7/2||Cristiano Ronaldo is 7/2 with Paddy Power to win the Fifa Ballon d'Or award this year
The Spanish champions have responded to the outburst by releasing an official statement which threatens legal action against Godall.
"Real Madrid reject in the strongest disqualifications of the former vice president of Barcelona, Alfons Godall, toward our coach, Jose Mourinho, after the conclusion of Tuesday's meeting between our team and Manchester City," it reads.
"Real Madrid condemn this attack and we have instructed our legal services to undertake the legal action they deem appropriate.
"Real Madrid will not allow threats of this nature and will always act against those who violate the honour of those who are part of our club."
Godall responded angrily to Cristiano Ronaldo's last-minute winner in the Group D encounter on Tuesday and suggested Mourinho was compensating for his less-distinguished playing career by celebrating like a player as he slid on his knees following the winning goal.