Mitrovic, Fulham's top scorer in four of the last five seasons, did not play in the West London derby after being injured in the opening game of the season at Everton last weekend.
"I got information before the match and now the confirmation from the club after the match too that he's on his way to leave the club," the Portuguese told reporters at Craven Cottage.
"Both clubs they got an agreement and now is the moment to finish the era of Mitrovic in our club.
"He forced everything to leave the club, he wanted to leave the club," he added.
"In the end, they reached an agreement and now is the moment for us to keep playing and working without him."
Silva did not provide any details about the deal.
Mitrovic has three years left on his contract and Fulham last month reportedly rejected a 25 million pound bid from Al Hilal, who have also signed Brazil's Neymar from Paris St Germain.
British media reported that Riyadh-based Al-Hilal had since come back with a greatly improved offer of around 46 million pounds.
Silva said Fulham would seek to replace Mitrovic within the transfer window but it would not be easy.
"Unfortunately for me as manager, we have four or five players to sign in 15 days. The striker position and striker market is not an easy one," he said.
"Many clubs are looking for the same. We are going to do our best to do it.
"We have to find the right player to replace him. If not we're going to face the Premier League with the players we have here."
