The students are third in the premier two competition but are just two points behind Brighton and are already in the semifinal spot.
Brighton leads the competition on 45 points and is followed by Southern (44), University B (43), Dunedin (42) and Harbour (34).
The students were leading the competition but were beaten 24-23 by Harbour on Saturday.
Under the present rules, University and Brighton are the only teams able to challenge premier struggler Zingari-Richmond for its spot if they win the second-tier banner.
Otago University Rugby Club chairman Kelvin Fisher said his members had mixed views on whether to challenge for a premier spot in a promotion-relegation game.
University B dropped out of the top tier when it was beaten by a resurgent Taieri in such a game two years ago.
Taieri won 42-17.
The club has a lifeline as the Otago Rugby Football Union ruled in 2001 that University was the only club permitted to have two teams in premier rugby.
But now an ORFU amateur rugby review has suggested allowing only one premier team from each club.
That would mean the likes of West Taieri, Brighton and Eastern being allowed to challenge for promotion if they won premier two, but not University B.
"The amateur rugby review could force us into a decision that we might not have made," Fisher said.
"We would prefer to make a decision that best suits our club.
"The review process is forcing us to challenge for promotion this year to maintain our right to have two premier teams.
The amateur review wants to take that right away."
ORFU operations co-ordinator Richard Perkins said any changes would have to be approved at the annual meeting or at a special general meeting, and would not affect this year's promotion-relegation game.
Zingari-Richmond has not won any premier games this year - it has conceded 631 points in just 14 games - and is ripe for the picking.
"It is always on the back of our minds," Zingari-Richmond club captain Kenny Ball said.
"It is not a nice feeling.
"We have been riddled by injuries this year and it has been difficult to field our top team. It would be a disaster for our club if we went down."
Zingari-Richmond is one of the great clubs of Otago rugby and has been part of the Dunedin premier scene for 130 years.
Its All Blacks include Norm Wilson, Red Conway, Keith Murdoch, Duncan Robertson and Joe McDonnell.
The Metropolitan Committee last week upheld an appeal from Harbour, which was awarded the bonus point taken from it for playing a disputed player against Pirates in the fifth round of the premier competition.
Pirates lost its bonus point.
The Metropolitan Committee has ruled that the middle four teams will play-off for positions of fifth, sixth, seventh and eighth position over the next two weeks.
Green Island has been confirmed in ninth spot and Zingari-Richmond 10th.
Zingari-Richmond will be subject to any possible promotion relegation challenge.
Green Island and Zingari-Richmond will join Lawrence and Clutha Valley in a separate competition.
