The 24-year-old striker, who scored 25 Premier League goals last season, turned down the most lucrative contract offer in Everton's history in March.
"I don't want to stay at the same level. I want to improve and I know where I want to do that," Belgian Lukaku said on Monday.
Former club Chelsea, who he originally signed for in 2011, remain favourites to complete a deal for Lukaku.
The Premier League champions, Manchester United and Bayern Munich have been linked with a move for Lukaku, who has been at Everton since 2013.
"We are now talking to the club. I know what's happening, but I will leave the talks to my agent," he added to journalists after Belgium beat the Czech Republic in a friendly in Brussels.
"I know what's happening, but I can't tell you anything more.
"What I would like most is to play in the Champions League and try to win the Premier League once. Or better - a few times."
Lukaku is represented by Mino Raiola, the agent who helped negotiate Paul Pogba's £89m move to Manchester United last summer.

Maxwell Cornet controlled Alexandre Lacazette's pass to drive in an opener.
Sergi Darder added an exquisite second on half-time, controlling Rafael's cross and flicking it past Kevin Trapp.
Despite Lucas Moura's steered finish, PSG lost their first league game since last March, but still have a 23-point lead at the top.
Laurent Blanc's side had not lost a league match since a 3-2 defeat at Bordeaux 11 months earlier, but looked off the pace and struggled without the creative influence of injured winger Angel di Maria.
After Cornet's opener, PSG could have been reduced to 10 men, as midfielder Thiago Motta escaped with a booking for raising his fist to the side of Jordan Ferri's head.
The leaders' best spell of pressure came shortly before Darder made it 2-0, with Zlatan Ibrahimovic having a shot beaten out by Lyon keeper Anthony Lopes.
PSG rarely looked like equalising after Lucas scored, and the excellent Rachid Ghezzal should have added a third for the home side when clean through, but Trapp advanced from his line to block.
Monaco, in second place, end the weekend having narrowed the gap at the top, despite dropping points themselves in a 0-0 draw at Nantes.
Caen had moved above Lyon and into third earlier on Sunday by winning 2-1 at St-Etienne, with former Wigan striker Andy Delort among the scorers.

It relates to Vodafone's 2007 takeover of Hong Kong-based Hutchison Whampoa's Indian mobile unit for $11bn (Â£6.5bn).
Indian authorities have said the firm owes nearly $2.2bn in taxes over the deal, a claim the firm has disputed.
India's top court ruled in favour of Vodafone in 2012, but the government changed laws later that year to allow firms to be taxed retrospectively.
That development was criticised by investors and also triggered concerns among many foreign firms looking to enter India.
Vodafone's Dutch subsidiary acquired a 67% stake in CGP Investments Ltd, a Cayman Islands registered company which held the Indian telecom assets of Hutchison in May 2007.
Vodafone has long claimed that the deal was not subject to any taxes in India as the assets were held by a firm based in the Cayman Islands.
However, the Indian authorities presented it with a tax demand of 112bn rupees - equivalent $2.2bn at the time.
The Indian government subsequently also sought penalties of up to 100% of the original bill.
Everton's Romelu Lukaku has decided where he wants to play next season.
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Paris St-Germain's 36-match unbeaten run in Ligue 1 was ended as Lyon beat them to move into the third and final Champions League qualification spot.
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Vodafone has sought international arbitration to resolve its tax dispute with the Indian government.