The Ukrainian Premier League side head into the contest in Kiev on the back of a 1-0 victory at Karpaty - their ninth match without defeat in all competitions.
However, Dnipro were left counting the cost of key trio Egidio Pereira Junior, Yevhen Konoplyanka and Matheus Nascimento picking up knocks.
And Markevych admits Dnipro's injury woes are a concern ahead of their meeting with the Dutch champions.
"There's nothing to say about whether we are ready for that game," he told reporters.
"Egidio, Yevhen Konoplyanka and Matheus are all struggling with injuries. We have many problems."
Dnipro's options are further depleted by the fact that midfielder Jaba Kankava will sit out through suspension.
While Dnipro may be up against it, they have shown their ability to mix it in Europe's secondary competition this term.
Having come through a difficult group that included Inter and Saint-Etienne, Dnipro then defeated Olympiacos 4-2 on aggregate in the round of 32.
But Frank de Boer's Ajax have been the dominant force in Dutch football in recent years, having lifted the Eredivisie title in four consecutive years.
That run is in jeopardy this season, though, with PSV holding an 11-point lead at the top of the table with just eight league games remaining.
And De Boer, who recently stated that securing second place is his primary focus in the league, may see the Europa League as the last chance to collect major silverware this term after they were eliminated from the KNVB Beker in December.
Ajax endured a disappointing Champions League campaign, winning just once in six group-stage fixtures.
But a comfortable 4-0 aggregate victory against Legia Warsaw in the Europa League round of 32 showed that they could be a force to be reckoned with.
Striker Kolbeinn Sigthorsson (knee) is a doubt for the trip to Kiev, but De Boer is able to welcome fellow forward Arek Milik and captain Niklas Moisander back to his squad.
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