She was also publicly critical of the process for the first time.
"He had certain information in front of him. Now we have contradictory information in the public domain. Of course that's not good enough."
Last week, Lees-Galloway told Parliament he would be reviewing Sroubek's case after "new information" had been made available to him.
In the subsequent days, a High Court judgment revealed that Sroubek had been back to Europe in 2009, undercutting any belief that his life might be in danger if he was deported.
Lees-Galloway said this week he was not aware of the court judgment and said it was not standard practice to have all court decisions relating to Sroubek handed to him.
It was also revealed the Czech Republic wanted to extradite Sroubek, who had an arrest warrant in the country for outstanding criminal proceedings.
Ardern told Newstalk ZB this morning officials are looking into a number of issues.
She said not everything officials need to consider about the case was strictly confined to Sroubek's travel back to Europe or his use of a false passport.
"Once [the new report] comes in, then we will look at what issues we have with the system generally because we can't have a situation where the minister doesn't have everything in front of them or a situation where officials don't have everything in front of them."
Immigration officials told Lees-Galloway last week that they would deliver their findings in three weeks' time.
But Ardern was not impressed with that timeframe and agreed with Lees-Galloway that the information needed to ready much sooner.