Calls have been made to move next year's Africa Cup of Nations away from Morocco following the spread of the virus, with Ghana and South Africa said to have been suggested as potential hosts for the tournament.
However, a series of qualifiers were played right across the continent this week, which has left Klopp questioning football's major governing bodies.
"I don't know whether the players think about [Ebola], but I think a lot about it," the 47-year-old is quoted as saying by Goal.com. "I spoke a lot with [Pierre-Emerick Aubameyang] about it, tried to sensitise him of the problem as he was away with his national team.
"Young people are green; they don't think that much about such things. I don't really understand how FIFA or whoever is responsible for that can assume that of all things the borders in Africa are safe enough that no Ebola-infected person can travel to another country. Even [in Europe], we aren't able to do that.
"If there is one country in Africa which has the feeling that it can't host the cup safely then this has to be the priority, not the Africa Cup. You have to take this seriously and can't shut your eyes. There will be a lot people from all over Africa in Morocco to watch the games and only a few of them would have undergone the best medical checks."
The 2015 Africa Cup of Nations is scheduled to get underway on January 17.