Rooney said he was staying with Manchester United following persistent speculation he could make a lucrative move.
Everton manager Ronald Koeman paved the way Tuesday for Wayne Rooney's return to the club of his youth by saying he would make the side "stronger".
Last week Rooney said he was staying with Manchester United following persistent speculation he could make a lucrative move to the Chinese Super League.
But doubts still surround the long-term club future of the 31-year-old Rooney, the England national side's record goal-scorer, and Koeman appears ready to try to bring him back to Liverpool-based Everton.
"I believe that Wayne Rooney is still playing at a high level," Koeman told Sky Sports.
"I think he made a good choice to stay at Manchester United and in the Premier League because he has still two or three years in front of him to play on a high level," the former Dutch international added.
"What will happen at the end of the season? I don't know but in my opinion he is one of the players who can make Everton more stronger."
"It's all about what the player likes, what Manchester United needs to do, and we are not involved in that project."
"But every player that we at Everton think can make the team stronger is welcome to Everton."
'Class apart'
Steve Walsh, Everton's director of football, endorsed Koeman's comments, adding: "Wayne Rooney is one of the greatest players that has ever played the game in England and for us not to be interested would be wrong."
"He started his career here and if the opportunity arose that he could come back and it sat well with everyone it is something we would consider."
"He is a class apart, he sees things, and all the things that have been said about Wayne are true. He comes into that category of being one of England's greatest ever players, so why wouldn't we be interested?"
"But let's not get ahead of ourselves. Wayne is contracted to Manchester United and made a decision to continue to play for them."
"Let's wait and see what happens in the future."
Rooney, born in Liverpool, joined Everton as a nine-year-old and made his senior debut aged 16 on the opening day of the 2002/03 season against Tottenham Hotspur.
Six weeks later, Rooney became Everton's youngest scorer with two goals against Wrexham in the League Cup.
Rooney catapulted to national attention when he scored his first Premier League goal -- a last-minute winner against Arsenal -- five days before his 17th birthday.
The 18-year-old Rooney left Everton to join United in a £27 million ($34 million/32 million euros) move in 2004.
He has since won five Premier League titles and a Champions League trophy with United and become the club's record goal-scorer.
Speculation about his Old Trafford future has intensified since Rooney ceased to be a first-team regular under manager Jose Mourinho. That was heightened when he was left on the bench for Sunday's League Cup final win against Southampton at Wembley.
