"If he shows his commitment to the team, the club and the fans (then) even not signing a new contract is no problem for myself", Koeman said.
With nine games remaining, that total is still in Lukaku's sights as he aims to cement his position as the Premier League's top scorer. They say she discussed her son's desire to play in the Champions League and advised him to make snub a new deal in a bid to force a move this summer.
"Just buying better players doesn't mean you will play in that tournament, because Manchester United, City, Liverpool or Arsenal won't qualify and they spent money for that".
Lukaku added that despite the club's progress under major shareholder Farhad Moshiri and manager Ronald Koeman, Everton had failed in its pursuit of several transfer targets.
Asked if if hopes he can keep hold of Lukaku, the Everton boss told BBC Sport: 'You need to have hope in life!
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Lukaku has netted an astounding 19 goals in the top-flight this season, and is showing no real signs of sowing down.
One of them, 20-year-old Dominic Calvert-Lewin opened the scoring after eight minutes on Saturday with his first Premier League goal - turning in a cross from teenager Tom Davies.
Whatever the Belgium striker decides, the future looks healthy for Everton with several young gems emerging.
However, a harsh decision by referee Paul Tierney to dismiss Tom Huddlestone for a lunge on Idrissa Gueye enabled Everton to wrap-up the points in style late on, although Koeman acknowledged that Hull presented a tough challenge. We have had a great run at home. "But the final result didn't reflect what happened on the pitch", Koeman added.
"He scored his first goal but it's a whole team performance that matters".