Kompany lifted his fourth Premier League title as City captain on Monday (NZST), after Pep Guardiola's side beat Brighton and Hove Albion 4-1 to finally see off Liverpool's challenge.
The 33-year-old scored a stunning goal in the win over Leicester City in the penultimate game of the season, setting his team up for its final-day victory at the AMEX Stadium.
Portugal playmaker Silva, meanwhile, has enjoyed a fantastic season for City, scoring seven goals and providing as many assists in the league this term.
And Kompany believes the 24-year-old has all the attributes to become City's leader in years to come, as long as he cuts down on being the class clown.
"I say to him often you are 50 per cent clown, 50 per cent leader," Kompany said.
"When he becomes 25 per cent clown, 75 per cent leader he will become the captain of this team.
"He is so strong and to be honest there is nobody who deserves this title more."
Silva's superb campaign was reflected by his nomination for the PFA Players' Player of the Year Award – which was won by Liverpool defender Virgil van Dijk – and his inclusion in the PFA Team of the Year.