Romelu Lukaku scored one of the great Goodison goals of the modern era against Chelsea in the FA Cup quarter-final last weekend but it could well prove one of his last for the club after the Everton striker gave his strongest hint yet that his future lies away from Merseyside.

Ahead of Saturday's lunchtime meeting with Arsenal, Lukaku said that “Champions League football is really the next step” after a season he could well end as the first Evertonian to break the 30-goal barrier since Gary Lineker in 1986.

“I am 23 this summer,” he said. “I have been playing since I was 16 and I never had a taste of the Champions League. It is going to be seven years now [as a professional]. You think about it.”

That Lukaku has sky-high standards is evident from the fact that, speaking at the club’s training ground this week, he gave himself a mark of just “eight, maybe eight and a half” out of 10 after his Ricky Villa-style dash through Chelsea’s defence last Saturday.

These same standards mean he does not hide his frustration over a campaign of underachievement from 12th-placed Everton in the Premier League. “I’ve been saying it for weeks – we’ve been underperforming this season. We don’t need to lie, that’s the truth.”

Lukaku, Everton’s £28m club record signing from Chelsea two summers ago, has three years remaining on his contract but last summer acquired a new agent in Mino Raiola, whose clients include Paul Pogba and Mario Balotelli.

Although Everton’s new major shareholder Farhad Moshiri, the Iranian-born billionaire, announced last week his ambition of “retaining our key players”, Lukaku’s comments suggest he could well face a losing battle in trying to hold on to the Belgian.

Champions League football is really the next step. You think about it <p> </p>

“If something happens, it will be for the good of the club,” Lukaku said of the prospect of a transfer. “I don’t want to leave in a fight, if it happens. I don’t want to say this or that – it is going to be good for the club and good for me personally because, at the end of the day, they were the ones who believed in me at the time when nobody believed in me, and they gave me a platform to perform.”

Lukaku believes he has reached a new level over the past 12 months. “I have been playing since I was 16 so at a certain point you have to make that step into the player everyone expects you to be,” he said.

“At one point last season I was thinking, ‘Am I doing enough?’ Because I’m really fast, really strong, and can score with both feet and with my head but I was too inconsistent. From January last year, everything changed but I really had my eyes on this season. Maybe I have proved the doubters wrong by playing like I am. It’s come at the right time. I’m 22 now. This is like a transition year for me. This is the base and then I don’t look back.”

The question marks surrounding Lukaku’s future are magnified by the fact his progress has not been matched by Roberto Martinez’s Everton team, despite runs to both domestic cup semi-finals. “We should have at least been in the top four this year because of the way the league is this year,” Lukaku said. “You look around the dressing room and wonder how the hell we are in this position.”