McEachran, 17, has emerged with the Stamford Bridge first team this season and made his Premier League bow in the defeat to Manchester City earlier this month. The highly rated youth international has Scottish lineage and the nation were believed to have made overtures to use him north of the border.
Speaking to the Daily Record, Stark revealed he had made no move for McEachran and would need "some encouragement" to make an offer.
"Of course I'm aware of Josh but he's playing for England and there's nothing to suggest he's unhappy with that situation," Stark said.
"He's playing for England and that's it as far as I'm concerned. If someone is currently playing for another nation we'd have to be given some encouragement."
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