If he does go, Everton will need to make big-name signings, especially with Romelu Lukaku now also seemingly destined to depart the Merseyside club.
Koeman said: "I don't think so - if the player shows his commitment in his football".
Mourinho managed Lukaku during their time together at Chelsea, but ended up selling him as the player struggled for game time at Stamford Bridge. Whatever type of situation, I just try to deliver.
"But OK, he is young. he can make mistakes".
The manner in which one grateful fan gleefully accepted Lukaku's shirt when he hurled it into the crowd at the final whistle showed his harsh words have not affected his popularity - helped of course by his goals.
Lure of the All Blacks hits Jones
The All Blacks will also play the British and Irish Lions in June and July, coming up against a number of Jones' English men. NZR boss Steve Tew was coy in the report, saying: "It's highly unlikely at this stage".
However Koeman still believes that catching Jose Mourinho's Manchester United, who are in sixth and seven points ahead of Koeman's men, will prove Everton's ambition to join the Premier League's elite. "We're in a good position in this project and you don't sell your best players".
Everton are sixth in the Premier League table at the moment with 50 points from 29 matches.
Lukaku, who is the joint top-scorer in the English Premier League with 19 goals, has told Everton he will not sign a new deal which would have made him the club's first £100 000-plus-a-week player.
"We try to get the best players, but a lot of them want to play Champions League and we are not playing Champions League at the moment". A lot. But two of them will not be in there. We know he is one of the best.
Liverpool-based Everton last won a league title in the 1986-87 season, when it was crowned champion of the old First Division, and the club's last major trophy was the 1994-95 FA Cup.