The 23-year-old has been suffering from a calf strain and did not travel with the rest of Koeman's squad to Dubai earlier this week for a warm weather training camp.
David Moyes remained upbeat following Sunderland's defeat at Everton, but admitted he was disappointment with the two goals his side conceded at Goodison Park.
Lukaku created an opportunity for himself late in the second half after powering past Darron Gibson before blasting a right footed shot a tad too close to Pickford, allowing the Sunderland stopper to parry safely away from goal. "Sunderland have been in that position quite regularly and we have the players to deal with the situation".
"I wanted to keep them quiet and keep the game at a low level".
Everton were dominant in the first period and deserved their 1-0 lead at the break, after Idrissa Gueye scored his first goal for the club with a well-taken finish.
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The 6f 10in former LSU standout, who was born in Melbourne, was Philadelphia's first No1 overall pick since Allen Iverson in 1996. But there was always the outside chance that it didn't happen because there wasn't complete or full healing.
"I told them that and told them to take the ball more and be a bit braver". I was disappointed we lost the first goal.
With Liverpool not playing until Monday, Everton could go just five points behind their Merseyside rivals in the table if they beat Sunderland on Saturday, and also carry on their eight-game unbeaten run.
Everton then hit Sunderland on the break, scoring a second through Romelu Lukaku to seal the win ten minutes before the end.
Moyes said the game against 7th-placed Everton was always going to be a hard one and insists he doesn't think his Sunderland side are far away from a winning run. If it was not one of Lukaku's prettier goals, it was the type of opportunity few other forwards would have been able to accept. Lukaku showed speed, strength and determination in homing in on goal, as well as the ability to force the ball past Pickford.