Lukaku's time on Merseyside looks set to come to an end after the Belgium striker refused to sign a new contract at Goodison Park, with his current deal still having two years left to run.
Former club Chelsea have been linked with a move to bring Lukaku back to Stamford Bridge, while United are reportedly looking at their striker options after Zlatan Ibrahimovic suffered a serious knee injury in the Europa League tie against Anderlecht.
A move to Old Trafford would see Lukaku reunited with Jose Mourinho, who sold him to Everton while manager of Chelsea, but Koeman aimed firing shots at the Red Devils and claimed Lukaku will not fulfil his wish of playing Champions League football at United.
"I cannot see Manchester United finishing in the top four. Zlatan's injury looks bad and when I look at the amount of matches they are having to play this season I can see them missing the top four," Koeman said.
"I have not been impressed by the way they play.
"They are struggling to decide matches. With Everton we drew twice against United this season and both times there was more in it for us.
"The Europa League is a different calibre than the Champions League. The fact that Man United were struggling to beat a team like Anderlecht proves what kind of season the club is having."
Despite Lukaku, who has 24 Premier League goals this season, having seemingly made his mind up over a move away from Merseyside, Koeman insists Everton are under no pressure to sell.
"Everton now have the resources to keep every player, including Lukaku, who has a contract for another two years," he added.
"I am talking to the owners every week. We want to make the next step with this club towards a higher level.
"A lot is possible here and we want to bring in the best players we can get, players who will help us to play for a place in the Champions League.
"For next season we need a bigger squad anyway as we will be in Europe again. But keeping our best players is a prime target for me. We are doing everything we can to hold on to top players.
"I have been there as a player too. I know what it is like when a player has big ambitions.
"But if we really want, we can make the players stick to their contract. That decision will eventually be made by the board."