"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.
Arsenal Edge Leicester in 7-Goal Premier League Thriller
But Leicester , which so astonishingly won the league in 2016, couldn't hold on for its first win at Arsenal since 1973. We had some avoidable goals which we conceded and overall we have to work on that".
"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.
'Jersey Shore' gang reuniting for an E! special August 20
Along with the premiere date, E! has released some sneak peeks of the upcoming docu-series. The clip ends with Sorrentino saying he and Pauly haven't spoken in five years.
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".
Korean tensions keep yen near eight-week highs
Toyota Motor shares fell 1.6%, Honda Motor shares fell 1.2%, TDK Corp. shares lost 2% and Advantest Corp. shares were down 2.6%. Ben Cardin, the Foreign affairs committee's top Democrat, compared Trump's comments to those issued by North Korea itself.