Silva, who is on loan from AC Milan, has featured 27 times in LaLiga this season but has not played since 4 April, while his most recent start came on 17 March.
The 23-year-old's LaLiga stay began brightly with a hat-trick on his league debut against Rayo Vallecano, but the goals started to dry up in October.
A knee injury has kept him sidelined for almost two months, but Sevilla is reportedly concerned that he could be delaying his return to action in order to keep himself fresh for Portugal's UEFA Nations League finals campaign in early June.
Caparros believes Europe's governing body should support the club that pays his wages and intervene if Portugal attempts to name him in its squad.
"Andre Silva won't be ready [to play against Atletico Madrid on Monday AEST]," Caparros said.
"This a matter to discuss, because he had a good start to the season and now he's gone two months without playing.
"I imagine that for the good of the Portuguese national team they will not call him to play. It would be bad for him and his recovery.
"How would we – the fans, the board, sports management, and president – react if we saw him playing with his team at the beginning of June?
"I hope Portugal don't call him and that they respect our reports. He has an issue with his patella that is being treated.
"I don't think they'll call him up. If this is the case [Portugal do include him], UEFA should intervene so the medical report of the team that is paying him prevails.
"The only thing that would see the player's reputation called into question is whether he ends up with his national team at the beginning of June. We are not stupid."
Although Caparros insisted earlier in the season that Sevilla was almost certain to trigger the reported €35 million ($56.2 million) purchase option it has on Silva, that now looks unlikely given his form, the club's frustration with his injury problems and the impending arrival of Munas Dabbur from Salzburg.
Portugal faces Switzerland in the UEFA Nations League semi-final on 6 June (AEST).