The coach, who worked closely with the Portuguese star at Real Madrid and has come up against the Argentine many times, thinks both players are already legends
The likes of Pele, Diego Maradona, Zinedine Zidane and Brazil striker Ronaldo have gone down in the annals of history as both World Cup winners and stratospherically iconic players of their time.
Both attackers are taking their third attempt at becoming world champions this summer and, should either succeed, they are bound to be remembered for their heroics in Brazil at the end of their careers.
However, the Chelsea boss, who coached Portugal's Ronaldo at Real Madrid and faced Argentina's Messi countless times in his clashes with Barcelona, does not think it matters if they fail to win, though admitted it would put them among a privileged group.
"Messi is great, I don't think he needs to win with Argentina to be great," Mourinho told Yahoo. "Ronaldo is great, I don't think he needs to be world champion with Portugal to be great.
"But Maradona did it and Zidane did it and Ronaldo Nazario and Rivaldo did it. Many of the big guys did it, so everybody's waiting for them to do it."
Messi will face Bosnia-Herzegovina, Nigeria and Iran with Argentina in Group F of the World Cup finals, while Ronaldo will hope to navigate Portugal out of a tough group containing Germany, Ghana and USA.