"You have teams like Manchester City and Manchester United who will be stronger than last season, but it is still not the end of the transfer window".
Jordan Pickford, Michael Keane, Cuco Martina, Davy Klaassen and Sandro Ramirez should all make their Premier League debuts for the club while Wayne Rooney will also likely earn a start despite some disappointing performances in the Europa League qualifiers.
Everton have had deals worth up to £40 million and £45 million rejected for the Iceland midfielder this summer but Koeman said: "We are close".
Lukaku hit 25 league goals for Everton last season and, with supply coming from the likes of Juan Mata and Henrikh Mkhitaryan, the Belgian should record a similar tally.
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"First of all we have big ambitions", said Koeman ahead of Saturday's league opener at home to Stoke.
Lukaku offered Everton pace in behind opposition defences and has scored the majority of the club's goals in recent seasons - something that will need to be replaced if the Merseysiders are to progress.
"Okay, I believe if we get the picture of the last players we are stronger than last season but being stronger than last season does not mean you will win against the big six because they also will be more strong than last season".
"We can improve and spend money but everyone can improve and is spending money".
Lawrenson added that he is looking to see a better start to the season for Stoke having struggled early on last season, but he isn't seriously anxious about their fortunes this season.
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The delegation asked the premier for their political freedom, and demanded to get their closed offices reopened. During the meeting, issues concerning law and order and development came under discussion.
But the manager concedes that, for all Everton's shrewd business, it may only allow them to stand still, at least in terms of league position. "All being well, he should be with us today (Friday) at some point and hopefully we will get that done".
The former Barcelona man has proven that he is an ambitious man ready to take the path less travelled in pursuit of a better career and the move to Everton bodes well for his development.
Everton manager Koeman believes Barkley will leave Goodison Park this summer but insists the club will not be hostage to a deliberately late, undervalued offer for the midfielder.
"They've brought good players in but lost key players too, like Lukaku".
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