Garner last boxed in Southampton at a hotel show in 2017 and has also fought at the city’s Guildhall which can hold 1,749 people.
“We’ll have to have a word with Frank, I think, because the turnouts are getting better each time,” Garner told BBC Sport.
“It felt like the Southampton fans took over the O2 – I need a homecoming now, let’s get something on.”
Portsmouth’s Chamberlain, meanwhile, next fights at Wembley Stadium in September on the Riyad Season London event headlined by Anthony Joshua facing Daniel Dubois for the IBF heavyweight title.
Chamberlain’s past two fights have taken place in Saudi Arabia, winning both to extend his record to 16-0, including 12 knockouts.
“I’m delighted for Mark and his career so far.” promoter Warren added. “I’m sure he will take every advantage of the opportunity and platform in September.
“Let’s try and get all three of these guys together and on a show down in the south because that would be fabulous.”