The winger is a big-money signing from Crystal Palace this summer.
The winger completed a move to Merseyside earlier this week in a big-money switch from Crystal Palace.
The Blues have paid through the nose for the DR Congo international, with the deal set to cost over £30 million based on add-ons.
Manchester United's Michael Carrick and Crystal Palace's Yannick Bolasie
Koeman is clearly a fan, having seen the winger become a Premier League star during his time with the Eagles.
However, he has insisted that Bolasie must improve the number of goals he scores if he is to be a star man at his new club.
“He has a lot of strengths but he needs to improve in his productivity. Nine goals in three Premier League seasons is not a lot - it is too little,” he told the Daily Mail.
Crystal Palace's Yannick Bolasie in action with Reading's Jake Cooper
It remains to be seen if Bolasie can improve under Koeman and become a star at Everton this season and beyond.
He arrives at Goodison Park with a lot of expectation on his shoulders, with the Blues faithful expecting the finished package given the money the club has paid to sign him.
Should he quickly establish himself though and become the key player they are hoping he will be, then it is likely that price will be long forgotten by the end of the season.
Crystal Palace's Yannick Bolasie