The Spaniard is nursing a knock after his heel was caught in the second half of Everton's 1-0 win over Stoke City on Saturday.
Ramirez did not take part in training today, but Koeman has not completely ruled the forward out of contention.
"Sandro got a knock on his heel last Saturday and we need to wait until tomorrow (Thursday) to see if he will be available," Koeman told evertontv.
"He did not train on Wednesday and if it is not better, he will not play. It is not really serious, the question is more yes or no for tomorrow, but normally there will be no question for Monday's game against Manchester City."
Ramirez is one of seven players to have joined Everton this summer.