The long-running saga involving the Spain international appears to be coming to an end after the Blues accepted a bid in excess of £50m from Atletico.
Personal terms have yet to be agreed but the 28-year-old, who left his native Brazil on Thursday to undergo a medical with his former side, is expected to finalise his "dream" move in the coming days.
Costa was deemed surplus to requirements by boss Conte at the end of last season, despite scoring 20 goals in 35 appearances as Chelsea won their second Premier League title in three years, but he claims that there is zero animosity between the pair.
"There's nothing of the sort there, I'm not upset with anybody, I have no bitterness towards anyone. Everything is cool," he told Splash News.
Asked about his relationship with Chelsea supporters, he added: "Everybody knows how much I love the fans."
Costa, who has not played competitive football in 98 days, spent four years with Atletico before joining Chelsea in 2014.