The Argentina defender was reported to have missed training on Tuesday to try and force a move to Manchester United but Carvalho insists he will not be forced into letting him go.
Rojo's performances during the World Cup have increased interest in his signature, and the Old Trafford club have reportedly agreed a deal to secure the 24-year-old.
In-demand forward Islam Slimani has similarly been punished - with Leicester City and Stoke City among those linked to the Algeria man.
Carvalho confirmed that both players have been disciplined by the club and will not feature in the opening weekend of the Primeira Liga against Academica.
The president hopes both players will respect their contracts in the Portuguese capital but did concede their actions could lead to departures.
"There are two players who are under disciplinary proceedings, which are Slimani and Rojo," Carvalho told the club's official television channel.
"Both have three-year contracts. Sporting does not give in to blackmail, pressures, interest of agents nor attitudes that disrespect the group.
"On Saturday they cannot play.
"Let's see how long this process will take, it may take a little time, could last a long time, but it will not be resolved by Saturday.
"The process may end with the departure of the players or they may end up having to fulfil their three-year contract."
