Should they be in the final XI for the start of the ANZ international series rubber they would join eight other father-and-son combinations to have played test cricket for New Zealand.
Rutherford's father Ken captained New Zealand in the 1990s, the same time Latham's father Rod appeared for his country.
The absence through a thumb injury of Martin Guptill means two new openers will be needed for Dunedin.
Peter Fulton, 34, last played for New Zealand in 2009.
He, too, was in South Africa but injured a knee and returned before the two tests. He still has some issues with the knee but coach Mike Hesson is confident they won't prevent him playing in Dunedin.
Latham, who has played ODIs and T20 internationals, impressed for the New Zealand XI in their T20 games against England in Whangarei and is rated among the more talented young players coming through. However he has spent little time at the top recently.
Rutherford has played against England more on this tour than any other player. The Queenstown game will be his eighth appearance in nine matches.
Rutherford and Latham are effectively batting for one spot in that game, and Hesson confirmed yesterday Rutherford has the inside running to partner Fulton.
Hesson confirmed he and national selection manager Kim Littlejohn thought hard about promoting wicketkeeper BJ Watling back to the opening role, but his strong numbers since moving to the middle order mitigated against that.
Prolific Otago opener Aaron Redmond, who has scored more than 900 Plunket Shield runs this season, but has been unwanted by the national selectors since 2008, was also considered.
An additional fast bowler will be added to the squad after the completion of the warm-up match at Queenstown.
New Zealand: Brendon McCullum (captain), Trent Boult, Doug Bracewell, Dean Brownlie, Peter Fulton, Tom Latham, Bruce Martin, Hamish Rutherford, Tim Southee, Ross Taylor, BJ Watling, Kane Williamson.
