Cairns (39), who was most recently aligned to the unsanctioned Indian Cricket League twenty/20 competition, is among 97 players including Otago pair Nathan McCullum and Ian Butler chasing a contract.
The players will learn tomorrow whether they have been included on the final auction list.
The eight franchises then bid for those players on January 19.
McCullum and Butler played crucial roles for Otago in its successful domestic twenty/20 campaign last season and in 12 twenty/20 internationals the bowling all-rounders have complied useful records.
McCullum, an offspinner, has taken nine wickets at 17.66 and has been frugal, going for 6.53 runs an over.
Butler has taken 16 wickets at 20.75.
Both are handy lower-order batsmen.
Butler, in particular, can hit a long ball and McCullum might get some extra traction trading on the name of his younger brother, Black Caps wicketkeeper-batsman Brendon McCullum, who set the IPL alight with an incredible undefeated innings of 158 for Kolkata in the inaugural match.
Shane Bond also features on the list of nine New Zealand players seeking a contract through the third IPL auction.
A former ICL rebel, the 34-year-old made a successful return to international cricket last year though injury forced his retirement from the test format after a man-of-the-match-winning performance against Pakistan in Dunedin last month - his first cap in two years.
Daryl Tuffey, who also made his comeback to test cricket against Pakistan after severing ties with the ICL, is also keen to join a franchise.
Lou Vincent, another former international with ICL history, has also put his name forward for consideration.
New Zealand is already well represented in the IPL with Daniel Vettori, Jacob Oram, Scott Styris, Brendon McCullum, Ross Taylor, Jesse Ryder and Kyle Mills signed up.
Outside of Bond, batsman Martin Guptill might hold the greatest appeal as a hard hitter at the top of the order.
Cairns, who made his debut against Australia in 1989, played the last of his 62 tests against England in 2004.
He also played 215 one-day internationals before wrapping up the limited overs component of his career with a twenty/20 game against the West Indies in 2006.
The number of overseas players a franchise may have on its roster is capped at 10 and at present it is unclear how many slots are available.
In 2009, more than 100 players registered for the auction, out of which 50 went under the hammer to fill 17 available overseas slots.
The number of places could be substantially lower this time.
Other former internationals to have registered include former Pakistan spinner - and occasional New Zealand assistant coach - Saqlain Mushtaq, and Australian batsman Damien Martyn.
