Posh hope to unveil their new stadium on the Embankment in January 2023.
Previously, the club has spoken about the ground having capacity for 17,500 fans - potentially rising to 23,000 – with the option for safe standing.
But speaking to Posh press officer Phil Adlam, Mr Thompson made reference to a capacity of 19,500 which he said had drawn scepticism from supporters who felt the number was too ambitious.
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The current London Road ground, which Posh are on the verge of buying back from Peterborough City Council, has a capacity of 14,100.
However, the new stadium, which has been inspired by the Groupama Arena in Budapest, Hungary, and which will be owned by the club’s three co-owners, will have a huge focus on non-football events with Mr Thompson aiming for 280 functions a year.
This includes exhibitions, wedding events and concerts.
Mr Thompson said: “I might troll Twitter or a couple of the fan forums and there’s a lot of pushback on the 19,500 which is interesting to me.
“To us, if you build a stadium and put a team of players together - you bring people into this new community - 19,500 is pretty easy in some ways. It’s not that much bigger than London Road.
“But again, this centre we’re building is not just a stadium. If you think about an inverted triangle, the stadium is at the bottom. At the top you have what’s going on 280 days a year.
“We’re working with the cultural community, we’re working with the Key Theatre on the other side (of the river). We’ve got community sport - the (new) university is going to be a big user of the stadium, I believe.
“That means the football component of that community centre is actually quite small, and therefore we’re less fussed about the 19,500. I’m more stressed about the place not being used 280 days a year.”
Mr Thompson also said that the new stadium design should encourage a better atmosphere on matchdays.
He added: “What we loved about it is the fact it’s 19,500 compacted on top of each other. The rows are steeper. We’re going to try to bury the stadium as much as we can. i think that’s going to make a big difference to the noise level.”