Lukaku is the leading scorer in the Premier League this season with 24 goals in 32 appearances.
Antoine Griezmann and Romelu Lukaku are also wanted by United's league rivals Chelsea.
Everton boss has also spoken on the recent incident that saw Barkley punched in a Liverpool bar.
Dele Alli leads the race for the Young Player of the Season award.
Lukaku's future is very much up in the air.
Portuguese coach admits his current squad at Old Trafford is not good enough.
Barkley's current contract has just one year left to run.
The Everton duo exchanged words after the 1-1 draw with Manchester United.
Defoe and Lukaku have both been heavily linked with summer moves.
Lukaku and Williams were embroiled in a heated discussion at Old Trafford.
Lukaku is the Premier League's top goalscorer.
Lukaku and Barkley both flattered to deceive during the Merseyside derby.
Antonio Conte's men not planning to rest on their laurels this summer.
Everton have not won at Anfield since September 1999.
Lukaku, 23, has refused to sign a contract extension at Goodison Park.
Lukaku has been the subject of much speculation in recent weeks.
Toffees are ready to invest heavily in the summer.
Lukaku is the Premier League's top scorer with 21 goals.
Lukaku, 23, rejected a lucrative contract offer from Everton last week.
Lukaku's future is very much up in the air.
Lukaku's future has become a major talking point.
Lukaku has over two years left on his Everton contract and has rejected a new deal.