Lukaku, who recently became the Toffees' all-time top Premier League scorer with 62 goals, has been linked with his former club Chelsea.
The Belgian is now clear at the top in the race for the Premier League's Golden Boot, with two more goals than Tottenham Hotspur's injured Harry Kane, after extending his hot streak to finish off relegation-haunted Hull at Goodison Park.
If Everton's position in the table matched their form as the best in the division since the turn of the year, perhaps Lukaku would reconsider his stance on the thorny issue of contractual commitment, having announced this week that he will not sign a new one.
"I am a little bit anxious he will be out for several weeks but we need to wait for the scan to know what happened", Koeman said.
"We try to get the best players, but a lot of them want to play Champions League and we are not playing Champions League at the moment".
"We need the support, every player who is starting needs support".
Everton now reside in seventh in the Premier League standings, meaning Europa League football is still very much available for the club.
"See the difference between this season and last season. He (Barkley) needs to sign a new contract or you sell the player".
His double on Saturday, with both goals in added time, may not have been the decisive factor in putting the Toffees level on points with fifth-placed Arsenal, but it at least showed his professionalism can not be called into question.