The striker is expected to leave the Premier League champions after being told by Antonio Conte that he is no longer needed. A return to Atletico Madrid is Costa's preferred move, but he has complained that Chelsea are demanding too much for him.
Everton have recently emerged as a potential destination for the 28-year-old, who scored 20 goals in 35 Premier League games last season, as they look to add experience to their attack.
The £75 million sale of Romelu Lukaku to Manchester United has left them thin in the centre-forward position, with Wayne Rooney and 20-year-old Dominic Calvert-Lewin their only options.
And Koeman says Costa would be a good option to add competition for places in the starting XI.
"I have always said there will be a warm welcome for every good player here and he is a good player," he told reporters.
"We are still looking to bring in a striker. It is not about being unhappy with Dominic – I am very happy with him – but he is still young and we need more competition up front.
"We have tough fixtures and a lot of international players and a lot of players selected for the under-21s – six Everton players with England."
While Costa remains contracted to Chelsea until June 2019, his lawyers have begun legal action to force a move away from the club.
The Spain international has scored 58 goals in 120 games for the Blues since arriving from Atletico in 2014.