Last week's 1-0 win over Hawkes Bay was Otago's first home win of the season but it is still yet to log two wins in a row in the New Zealand Football Championship.
Fleming said the side needed another win to confirm its third position, with the chasing pack not far behind.
Otago is just one point ahead of Wellington on the table and will need a result tomorrow to stay in contention for the top four play-offs.
Only three points separate four clubs - Otago, Wellington, Canterbury and Manawatu - although the latter two clubs have a game in hand.
Otago may have a psychological edge, having beaten Wellington 2-0 early in the season when Dan Ede and Dave Dugdale scored.
Dugdale looked back to his best last week, but an injury cloud still hangs over Ede who injured his ankle at work.
A hamstring injury to Nathan Knox is also likely to be the object of a late fitness test, and the long-limbed striker may also miss this match.
However, the core of Otago's success has been the consistent performance of team captain Tim Homer and fellow defender Tom Sadd while goalkeeper James Waggett has allowed few clear opportunities at goal.
Wide defenders Tristan Prattley and Mike Abbott have also been effective and it would be a tough call for coach Fleming with Rhys Henderson returning keen to regain a starting slot.
New transfer window signings - Ben Light, from Victoria, Mike Smith and Harley Rodeka - will also make Fleming's choice a bit more difficult.
Against a classy Hawkes Bay side, Otago's midfield formed a hard-to-penetrate screen, as Andy Coburn and Robbie Deeley blunted the opposition, and Stu Kelly continued his trait of scoring winning goals.
Wellington has come back into form after a slow start to the season under coach Stu Jacobs.
The side from the capital logged three losses early in its campaign when it scored no goals and conceded seven.
Wellington though has recovered although it lost to top team Auckland 3-1 last weekend.
Six-goal Greg Draper has led the charge for coach Jacobs, who was injured last week when he rescued a dog that was being savaged.
He sustained 34 stitches during a three-hour operation.
If the Wellington coach can instill that same mental approach against Otago, then his team may not leave Carisbrook unrewarded.
With the Masters Games starting in Dunedin today, Otago United has offered cheap entry for the older spectators.
