The Dutch champions return to Amsterdam trailing 1-0 from last week's first encounter in Kiev, Roman Zozulya's 30th-minute strike proving decisive.
Ajax responded in superb fashion, though, with a 4-1 victory at Heerenveen in the Eredivisie - a result that left them eight points clear of third-placed Feyenoord.
Centre-back Veltman - who scored an own goal before making it 3-1 in that encounter - is aware that Ajax have made life difficult for themselves by failing to score in Ukraine, but believes the team have enough about them to make the quarter-finals.
"We could have made things so much easier if we had scored there," Veltman said.
"But we have not done that. It is very difficult now, but we still have a chance. The match against Heerenveen gave us confidence.
"Dnipro can come to us and play without attacking intentions. It is up to us to keep a clean sheet and score at least twice."
Ajax have been handed a further boost by the return of striker Kolbeinn Sigthorsson.
The Iceland international has been sidelined for almost two months by a knee injury, but he made a comeback in a reserve game on Monday and hopes to feature on Thursday.
"I wanted to come back as soon as possible," he added. "But it took longer than expected. The important thing is that now I can play again and it went well.
"I look forward to the next games. Hopefully on Thursday I am with the selection."
Dnipro followed up their win over Ajax by beating Metalurh Zaporizhya 1-0 in the Ukrainian Premier League.
However, head coach Myron Markevych must contend with three suspensions in Amsterdam - Zozulya, Ruslan Rotan and Artem Fedetskyi all picking up yellow cards in the first contest that will keep them sidelined.
Markevych opted to shuffle his pack in the victory over Metalurh with only Rotan of the suspended trio featuring during the match - a decision he admits was motivated by the fact he wanted to check his alternatives for the Ajax match.
"We have deliberately taken this step," he said. "Unfortunately, in the Europa League, we have only four defenders and one of them misses the match. So I took the opportunity to play other players.
"I could have used them [suspended players], but I had to see who can play in Amsterdam, who will be able to replace them."
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