McClaren claims he will have only an hour to prepare his squad for Wednesday's friendly against Germany because the majority of England's first-choice players are involved in matches on Sunday afternoon.
But the Premier League insist the Football Association were involved in the decision-making process over fixtures.
"It's disappointing to hear this because we worked very hard with the FA to accommodate the national team," Premier League spokesman Dan Johnson said in the Mail on Sunday.
"The FA were part of the fixtures working party along with the Premier League and the Football League.
"We can't micro-manage fixtures. If we had removed the Man City v United and Liverpool v Chelsea matches and put them somewhat else we might have created problems elsewhere.
"If anything, we feel for the clubs. They just get started then they are interrupted by a friendly international so early in their seasons.
"We would point out that there's an agreement in place ahead of competitive games."
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