The Toffees have made their best start to a campaign since 1978 under their new boss Koeman, winning four and drawing the other of their first five league fixtures to sit second in the table
Prior to Saturday's 3-1 victory over Middlesbrough, Koeman had said that while he was targeting European football for the club, the idea of them challenging for a Champions League spot this term was unrealistic.
And when the Dutchman was asked on Monday if Everton could emulate Leicester's achievement from last season by pulling off a surprise title triumph themselves this time around, he gave a similar response.
"Normally, we can't win the title - I think what Leicester did last season was an exception," Koeman said. "I don't think so.
"I am realistic
If I tell you we will fight for the title I think most people will say 'that man is crazy'
Even when I mention that, I'm not crazy?
"Why do we need to change our mind about our aspiration and ambition after 13 points from five games?
"The big teams have much more qualities and if they are not disappointed like last season it will be impossible."
Koeman was speaking ahead of Tuesday's EFL Cup clash with Championship side Norwich at Goodison Park.
And he confirmed striker Romelu Lukaku, whose goal in the Middlesbrough match made it four in his last two games, will sit out the third-round tie.
Koeman said Lukaku would rest after coming off in the second half against Boro with a toe problem, and that he expects the Belgium international to be back available for Saturday's league trip to Bournemouth.
The manager also signalled discussions have begun between Lukaku and the club over a new contract.
Koeman last month revealed the 23-year-old, who is currently on a deal that runs through to the end of 2018-19 and was linked with a move over the summer, had told him he had decided to stay "at least one more season" at Everton.
Koeman had at that point said it was "possible" Lukaku could sign a new contract with the Merseyside outfit.
And when asked on Monday about talk of negotiations now being under way, Koeman said: "The club are always trying to keep their best players.
"It's difficult but Everton are trying to keep him at the football club."
Enner Valencia is set to replace Lukaku on Tuesday, making his first start for the club, in what Koeman has vowed will be a "strong" line-up.
Meanwhile, midfielder Darron Gibson has been ruled out for three weeks following groin surgery.
Source : PA
Source: PA