The 23-year-old has been a transfer target for his former club Chelsea this summer but the Londoners have been reluctant to meet Everton's valuation of the striker - reported to be £75million
Lukaku has expressed a desire to play European football and was frustrated by Everton's 11th-placed finish last season in the Premier League under Roberto Martinez, but the Toffees were determined to keep hold of their biggest asset.
New major shareholder Farhad Moshiri wanted to convince the Belgium international of the project under Koeman, who was appointed in June, and the manager has revealed that Lukaku came to see him on Friday to tell him he plans to stay
"It is true
He spoke to me yesterday morning (to say) that he made the decision by himself to stay at least one more season at Everton and that is great news for everybody," said Koeman, speaking after Everton's 2-1 win at West Brom on Saturday
Asked if Lukaku might sign a new contract, Koeman added: "Yes that is possible."
Writing in his column for Dutch newspaper De Telegraaf, Koeman also said: "Lukaku is the top scorer, the target man and only 23 years old
Him staying at the club is just as valuable as a big transfer."
Lukaku did not start at The Hawthorns after recently having a heel injury but he was introduced from the bench seven minutes before half-time as Koeman responded to falling behind to Gareth McAuley's early headed goal by switching the formation.
The big striker impressed against the club with whom he enjoyed a successful loan spell during the 2012/13 season and Koeman dropped a strong hint that he will start next weekend's home match against Stoke.
"I was not doubting the player or his qualities
He was 10 days out with injury and he only did yesterday his second session, but I am not so stupid to put him on the bench next week
Of that there is no question," said Koeman.
"Today it was a tactical change, We started with three at the back as we did against Tottenham last week but we go a goal down and then drop more back and we needed a target man and to make the pitch more wide to create our own space and I think from that point on we were the dominant team."
Lukaku was not directly involved but the switch did quickly bring a reward as Everton equalised in the final minute of the first half.
A lovely one-touch passing move, started by Kevin Mirallas just outside the penalty area and involving Gareth Barry and Ross Barkley, was given the finish it deserved by Mirallas when he beat Ben Foster with a low shot from 12 yards out.
Barry headed the winning goal from close range after an hour but Koeman felt the timing of the equaliser was crucial.
He said: "Scoring just before half-time had a big impact on the final result, it was a key moment in the game.
"It gave a different situation for us in the dressing room and a different situation for West Brom
In the second half we were really good and played some good football and the substitutes played a big part in the final result."
West Brom boss Tony Pulis was left to rue the timing of Mirallas' strike and was upset by the manner in which his team conceded the two goals.
He said: "I thought we were the better team in the first half
I think they had just one shot that Gareth Barry steered straight at the goalkeeper
But then they scored in the 46th minute with 30 seconds to go, which is really disappointing, and it was a real kick for us.
"In the second half they were the better team and were able to bring on the likes of (Yannick) Bolasie but to concede from a set-piece is really disappointing because we are good at them.
"But I can't criticise these players because they work hard
What they lack, and sometimes they do lack things, they make up for with their effort and commitment."
Source : PA
Source: PA