The new head coach of the Portuguese side has stated that he believes the talented midfielder will not be heading to North London.
Carvalho has impressed for club and country over the last 24 months with his ability to dominate possession for his team, range of passing and positional play.
Despite the emergence of Francis Coquelin last season, the Gunners are still being linked with a host of midfield options to bolster their efforts at putting forward a title challenge next season.
Regardless of the link to the Emirates Stadium outfit, Jesus has said that Carvalho will still be in Lisbon next season.
"William is a certainty," ESPN quote Jesus as saying.
"Sporting has young people who are already certainties, are not hopes or doubts. William will be enhanced if the team is also.
"Only players value the team respond to winning titles. He's a player with features to play more. I have no doubt that with me will play more."
Carvalho’s performances for Sporting have seen him recognised at international level, with the deep-lying playmaker featuring for Portugal at last summer’s World Cup.
He was one of the standout players in this year’s under-21 European Championships, which will only have added more glowing scout reports to his name.