Costa is currently training alone in Brazil having been told by Blues boss Antonio Conte that he was no longer needed in west London.
The relationship between player and manager disintegrated following the break down of Costa's £76 million move to the Chinese Super League club Tianjin Quanjian in January,
Having failed to secure a move before the start of the 2017-18 Premier League season, though, Costa has now opened a legal case against the club in an attempt to force his departure.
Morata was signed as a replacement in a £70 million deal from Real Madrid after the club missed out on first-choice target Romelu Lukaku to Manchester United, and while Chelsea winger Willian is happy to have the 24-year-old at the club, he is sad to see his friend Costa leave.
"Everyone knows about Diego Costa's quality, the striker he is, and I am sad because he is leaving," Willian told Goal.
"He has not yet go to any club, but Morata, who has arrived, has quality and knows how to score goals too. Me and the other players are here to give all the support to our new players, for they can earn at Chelsea what they have been doing in their previous clubs.
"Matic and Diego [Costa] are two great players. I am sad to see them leave, but I expect Matic to be happy in his new club. But Chelsea have signed Bakayoko, who made a great season at Monaco, to reinforce our team."
"My relationship with Diego is very good. He has a way on the pitch, but he is a super good guy and very humble. He is a great friend who is unfortunately no longer with us. I only wish good things for him and all the luck in the world."
"I have great friends in Chelsea, like Diego and David Luiz. We [Willian and Luiz] are neighbours and we are always together in and out the field. Kenedy is also a great friend, and apart from the Brazilians, I have a lot of affinity with Hazard. I get along well with all the players. The atmosphere at Chelsea is very good."
Willian is entering his fifth season with Chelsea, claiming two Premier League titles in that time.
The 29-year-old was a key part in Conte's title-winning side last time out as the Blues secured 30 wins to set a new English top-tier record in a 38-game season.
Now, with rivals strengthening considerably in the summer, Willian believes it will be harder this time round and claims their participation in the Champions League this season could hinder their title charge if they fail to prepare correctly.
Asked who are Chelsea's main rivals for the trophy, Willian said: "I think all of them are rivals in the battle for the title. Of course, the battle for the title is always against five or six teams, but Premier League is a very difficult championship because you cannot predict any result. You know that the last placed team is as very tough opponent as the leader.
"This season is gonna be very different than the last season. The Premier League always gets better year after year. This year we have more games and the Champions League, so we need to be more attentive, because this season will be more difficult than the last."