The batsman sprained his shoulder joint while diving in the field during the second Test at Trent Bridge and appeared to be in discomfort when batting during England's second innings.
As a result, Flower confirmed that England will be picking cover for the 30-year-old unless he shows improvement before Saturday's squad selection.
"He is still in a bit of discomfort and nowhere near 100 per cent yet," said Flower.
"We will monitor his fitness as the week progresses and either provide cover or, if he says he is absolutely fine by Friday, there would be no need to provide cover."
England Lions captain James Taylor is currently favourite to replace Trott should the injury rule him out.