Messi, who was again said to be pressing for Enrique's exit after being benched in Barca's 1-0 defeat to Real Sociedad, has been linked with big-spending English giants Chelsea and Manchester City of late.
However, he maintains the talk is without substance.
"I never demanded anything to stay, as I have no intention of leaving," he told Barca TV. "It is not good to look for rivalry between Luis Enrique and me, because there is none.
"We must be more united than ever. They should not throw sh*t at us. We just want to achieve things for the club.
"I never demanded anything to stay, as I have no intention of leaving.
"It is said that my father spoke with Man City, with Chelsea. It's all lies, it's all lies."