Lukaku has made clear he wants to play for a club in the Champions League which Manchester United and Chelsea are able to offer him next season.
Earlier today the 24-year-old said he had an agreement with another club and his agent Mino Raiola knows what he wants.
Lukaku also insisted the prospect of staying at Everton was "not really an option".
Chelsea and United are the clear frontrunners to sign Lukaku but the Blues are understood to be leading the race.
Chelsea line-up next season including Romelu Lukaku Tue, June 6, 2017
Romelu Lukaku looks set to join Chelsea, but how could he fit into the team with Diego Costa?
Play slideshow AFP/Getty Images 1 of 11
GK: Thibaut Courtois
It is claimed Everton are interested in a potential swap deal involving players, in particular Sergio Romero and Chris Smalling.
Romero played second fiddle to David de Gea this season but impressed whenever he had the chance and started the Europa League final over the Spaniard.
While Smalling struggled to reach the heights of the previous season as injury hampered his form and Mourinho publicly criticised him over a perceived slow recovery from toe and knee problems.
Romelu Lukaku wants to leave Everton
Nevertheless Lukaku's Everton career appears to be over as he looks to join a top club in England.
Get Quotes on Home Insurance
He said: “Staying at Everton is not really an option for next season.
“I am staying calm about everything. There is nothing concrete with another club at the moment, but my agent is busy discussing things. I’m not going to make big declarations on my future, but I know where I want to play: in a club who are competing in the Champions League and can win titles in England. Staying in England is best for me. I know the competition, and I’ve almost reached 100 goals in the league, which is a milestone I want to achieve.
“The Premier League is a dream for me, but I also want to win the Champions League, the FA Cup and other prizes. I don’t want to stay at the same level. I want to improve, and I know where I want to do that.
“My agent is now talking to a club. I know where I want to go, so I’ll just stay patient. I know meetings have been arranged, so I’m just waiting for a call. We are now in discussions with the club. We’ll see what happens.”