Full-back Sime Vrsaljko is nursing a knee injury from the quarter-final success against Russia and was replaced by Vedran Corluka during extra time in Sochi.
Reports have suggested the 26-year-old is out of the last four clash in Moscow and could be replaced by Corluka from the start against Gareth Southgates side.
But Vrsaljko has told manager Zlatko Dalic he wants to play in Croatias first World Cup semi-final for 20 years.
Simeone is now trying to influence the decision over whether Vrsaljko starts and is insistent that the full-back be withdrawn from the clash, according to the Evening Standard.
The Atletico defender missed the last two months of the 2016-17 season with a similar injury and Simeone is concerned he could be absent for an extended period if his fitness is risked.
Dalic has shown himself to be a no-nonsense coach during this World Cup and sent home striker Nikola Kalinic is disgrace earlier in the tournament after he refused to play as a substitute against Nigeria in the group stage.
Kalinic complained he was suffering from a back problem – an excuse he had previously used during the friendly against Brazil and a training session before the tournament.
Vrsaljko played the full 90 minutes of the group wins over Nigeria and Argentina, but was rested for the success over Iceland.
He was then on the pitch for the full 120 minutes of the penalty shoot-out victory over Denmark before being withdrawn in the 97th minute against Russia.
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Along with Englands Kieran Trippier and Frances Benjamin Pavard, Vrasaljko has been one of the more effective right-backs at the World Cup and his absence will be a major blow for Croatia, who are bidding to reach the World Cup final for the first time.
Goalkeeper Danijel Subasic, who picked up a hamstring problem against Russia, and Dejan Lovren both missed training on Monday ahead of the game but are expected to be fit.
England have no injury problems ahead of the game after all 23 players trained following the win over Sweden. Jordan Henderson was complaining of a tight hamstring after the match but will be retained.