The airport wants to extend the runway by 164m (538ft) to facilitate the use of larger planes for holiday flights.
It has argued the plan is "critical to the airport's survival" and refusal by Eastleigh Borough Council would put more than 2,000 jobs at risk.
However, Southampton City Council and local campaigners have objected on the grounds of climate change and noise.
The city council upheld its objection after the airport submitted revised plans which it said included "significant mitigation" to noise and environmental impacts.
The changes included caps to passenger number growth and increasing the financial compensation for acoustic insulation to nearby households to £5,000.
Action group Airport Expansion Opposition (AXO) previously said more than 60,000 people would be exposed to increased noise from flights.
The airport previously said its existing runway was "one of the shortest in the UK" and inhibited the use of larger planes, such as Airbus 320 and Boeing 737.
Its planning statement said: "[It] precludes these aircraft types from taking off in a southerly direction when fully laden with passengers... and sufficient fuel to reach the key holiday market destinations of southern Europe."
The airport has said its plans would generate an extra £240m for the local economy by the year 2037.
Eastleigh Borough Council said members of the public could apply by 19 March to make short statements at the meeting, which would be streamed online.