The two men met at pitchside today to discuss next month's big fixture and Barwell is hoping the Saints fans can roar his team on to a second Heineken Cup triumph.
"I'm standing down as chairman in September and I said I wanted to leave having achieved two things - making a £1m profit and winning the Heineken Cup again," said Barwell.
"We are one of only two teams in the Premiership who actually make a profit, but the more immediate goal is to fill stadium:mk with Saints fans so we can help the team beat Ulster.
"That would mean a return to Milton Keynes for the semi-final against either Perpignan or Jonny Wilkinson's Toulon. It is a huge opportunity for the players, club and supporters.
"I am very envious of this facility in Milton Keynes and Pete has got a wonderful stadium for his team to play at. We are still battling to increase our capacity at Franklin's Gardens, but it is great to know there is a stadium like this to which we could possibly bring some more big games in the future."
Ulster, who are flying high in the Magners League at present, were the first Irish team to win the Heineken Cup in 1999. They finished as runners-up to Biarritz Olympique in Pool 4 to reach the last eight for the first time in 12 years.
"Ulster will be bringing almost 4,000 fans with them to Milton Keynes on Sunday, 10 April, but I'm looking for a full compliment of 18,000 Saints fans in the ground," admitted Barwell.
"We want to make this as much like Franklin's Gardens as we possibly can and create a wonderful atmosphere. The good thing about having to move the game is that we would only have had around 8,000 Saints supporters back home in Northampton, whereas now we can more than double that figure."
The Heineken Cup quarter-finals will see two major footballing venues get their first taste of European rugby action. Perpignan have moved their home game to the Olympic Stadium in Barcelona, while Saints have switched to Winkelman's League One team's venue.
"We want to host great events here at stadium:mk and this is certainly one of them. It is a proper use of this great facility," he said.
"We are making the stadium do more than it has done in the past and we want to show the rugby world that we can provide a stage for games at the top level."