Everton fans seem to have caught the optimism bug since Koeman's arrival on Merseyside a month ago, with a host of exotic new signings - notably Manchester United's Juan Mata (Telegraph) - tipped to follow, as new owner Farhad Moshiri prepares to put his money where his mouth is.
United's Mata would be a statement signing
And, according to Koeman's nephew Len - whose father Erwin is also the 53-year-old's assistant - the Iranian's ambition was very much part of the attraction.
"They have a new owner, the budget is over £100 million and so they can buy better players than they did at Southampton, who I don’t think have that money to invest (on players)," he said, as quoted by the Liverpool Echo.
"Everton is a big club and it is a new adventure, a new dawn.
"Before they went there (to Southampton), (the Tottenham head coach Mauricio) Pochettino came eighth and everybody said: 'Wow, this is amazing.' Then, two years in a row, they did even better than the season before.
"I think it would be really difficult to achieve better with Southampton. They would have to be fifth (to improve on the 2015-16 campaign) which is maybe difficult if you sell your best players."
The ongoing European Championship has understandably delayed Everton's progress in the transfer market, with only Maarten Stekelenburg - who played for Southampton, ironically, last season - arriving so far, from Championship side Fulham.
New recruit Stekelenburg wearing Southampton's colours
The speculation has not ceased, however, with the Toffees linked with moves for Belgium midfielder Axel Witsel (Mirror), Portugal goalkeeper Rui Patricio (Chronicle) and Netherlands defender Bruno Martins Indi (O Jogo), this week alone.
Belgium's Witsel is said to be a major Everton target