On January 8, New Zealand selectors Mike Hesson and Bruce Edgar must name their cup squad of 15.
On February 14, New Zealand play the opening cup game against Sri Lanka in Christchurch.
In between, New Zealand have seven ODIs against the Sri Lankans, two against Pakistan and two preparatory games against South Africa and Zimbabwe immediately before the tournament starts.
If the medical information is that Mills could be bowling again in, say, two weeks, that should not affect his selection chances. If Hesson and Edgar want him, they could pick him in reasonable expectation of full fitness for the cup.
However if the advice is poor, say five weeks off, it means either Mills would miss out, or he could be picked on the assumption he would be fit for the tournament, but without having had much preparatory game time.
Right now, it's all guess work until the selectors have something concrete to work with.
Spare a thought for Mills. Although he has raised the idea of carrying on after the cup if he felt he could contribute and was in good physical shape, the likelihood is that the tournament is seen as an ideal swansong for the 13-year veteran, especially with a coterie of younger fast-medium bowlers pressing hard.
If the news is grim for Mills, it may make selection more straightforward. There are six seamers - Tim Southee, Mitchell McClenaghan, Trent Boult, Matt Henry, Adam Milne and Mills - vying for, almost certainly, at most five places.
One option would be to pick four, bank on decent support from Corey Anderson and possibly Jimmy Neesham - which on current form is risky - and use the spare spot to ensure more batting depth.
New Zealand captain Brendon McCullum is to make a rare appearance for Otago in the third round of the Plunket Shield starting tomorrow.
McCullum will captain Otago against Canterbury at Rangiora, a good late opportunity for some red ball cricket before the first test against Sri Lanka starts in Christchurch on Boxing Day. He replaces Ryan Duffy in the only change to the side beaten by Northern Districts in the last round.
"Not only are we gaining an exceptional player but we are getting a guy who will bring a lot of enthusiasm, experience and a positive vibe to the dressing room," Otago coach Dimitri Mascarenhas said.
Among a group of six players not considered for the match due to injury is batsman Jesse Ryder, who has not played for Otago since November 13.