Over the past 24 hours, it has been reported that Wolves had become the favourites to sign Patricio, with new Napoli boss Carlo Ancelotti opting against a move.
Wolves appeared in line to sign the 30-year-old but it emerged that due to a change in the asking price, Patrico had tried to cancel his contract with the Portuguese giants in light of the recent attack on the first-team squad by a group of fans.
On Friday, De Carvalho made the call to address the situation in public and has claimed that Mendes is trying to secure a fee of €7m (£6.12m) from any deal involving Patricio and a previous transfer which saw Adrien Silva link up with Leicester City.
At a press conference, De Carvalho said: "What brings us here has to do with the arrival of termination of Rui Patrício's request.
"I want to tell you that Sporting were negotiating with Jorge Mendes, who said that there was a proposal from Naples, but in the meantime the change of the coach in the club ended up cooling that interest, then appeared Wolverhampton but that offer had different terms.
"Gestifute told us that they wanted €3m from Rui Patricio's business and another €4m from Adrien or we had no business. The money is not mine, it belongs to Sporting. Here we do the management of money as if it were ours. To accept giving a seven million to a man, whom we think is not entitled, we do not do it."
"It would be a crime against Sporting to accept blackmail like this. Sporting can not be under fear, under blackmail or under threat. I'm sorry that Rui has not talked to his employer about what is happening, to realise that he is being manipulated over things that have nothing to do with him.
"There are seven days by law for a player to reflect, and I hope Rui reflects. Someone is telling you a bad story. I hope that Rui has the possibility of leaving Sporting in a different way."
Patricio has spent the last 18 years at Sporting, having progressed through the youth team to make over 450 senior appearances.