There was speculation last week that the Italians had offered the 26-year-old midfielder to Everton in a £15 million deal.
Blues’ director of football Marcel Brands and Silva have drawn up a summer wish list in a bid to make a push for a top-six berth in the Premier League next season.
But, speaking to the Portuguese media, the Blues boss cooled suggestions of a move for Joao Mario, who he worked with while in charge of Sporting.
“He was my player, I was the one who put him in the main team of Sporting,” explained Silva. “He had a very good season, but at the moment he is not on the table.
“Joao is a player of Inter and there is nothing more than that,” Silva told O Jogo .
Joao Mario already has experience in the Premier League following a loan spell with West Ham during the 2017-18 season, when he made 12 starts, scoring twice.
He began his career at Sporting where he made his name and earned a £35 million move to Inter in the summer of 2016.
In all he has made 64 appearances for Inter, scoring four goals.
He has started 22 games for the Italian giants this season but scored only once as Inter prepare to go into the final game of the campaign against Empoli this weekend in fourth spot, 24 points behind champions Juventus.
Inter are widely expected to replace current manager Luciano Spalletti after two seasons in charge at San Siro.
Former Chelsea boss Antonio Conte has been strongly linked with the position and that could lead to big changes in the playing squad, including a departure for Joao Mario.
The diminutive schemer has 43 caps for Portugal, scoring twice and was a member of their 2018 World Cup squad.
Silva already has a fight on his hands to keep on-loan Barcelona midfielder Andre Gomes. He impressed for the Toffees this season and they are keen to make the deal permanent but Tottenham are believed to be monitoring the situation closely in the hope of attracting the Portuguese ace to London.