Ronald Koeman feels he would be perceived as "crazy" if he were to suggest Everton can challenge for the Premier League title this season.
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.
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.
Striker Nelson Oliveira is expected to make his Norwich debut at some stage during the game after building up his fitness since signing from Benfica last month.
Keeper John Ruddy, who has lost his place to Northern Ireland international Michael McGovern, may return with manager Alex Neil planning several changes.
Defenders Steven Whittaker and Sebastien Bassong, midfielders Sergi Canos, Louis Thompson and Josh Murphy as well as striker Kyle Lafferty started against Coventry in the previous round and could do so again.
Centre-back Ryan Bennett and playmaker Alex Pritchard, on the bench against Nottingham Forest on Saturday, will also be pushing to be in the starting XI.