Cairns' agent, lawyer Andrew Fitch-Holland - who gave evidence on his behalf at the 2012 trial - was arrested and bailed in March under suspicion of perverting the course of justice. The police have also taken statements from Vincent's wife, as well as another former teammate, Brendon McCullum.
Cairns is back in New Zealand.
On the two-week deadline, Cairns lawyer Aaron Lloyd told the Herald last night: "We've had no indication as to timing but that timing, in the next month, would be about right. It would be speculation, but it's pretty safe speculation as to the timing."
He said he had no indication of whether charges were likely.
Cairns' friend and former teammate Dion Nash told the Diary last month: "He's trying really hard and supporting his family the best way he can."
"He's not moping around, he's showing guts and doing hard work by cleaning bus shelters. All I can do is support him, but as a friend it is really hard to watch his name being dragged through the mud with no conclusion in sight. He's a champion guy and he will come through this stronger."
Modi's lawyer, Rajesh Vyakarnam, has made multiple trips to New Zealand in recent months. The last time, a fortnight ago, he was accompanied by an investigator.
The Herald understands Modi is preparing the ground for a civil case, regardless of whether Cairns is charged with perjury.