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Conte guided Inter to their first Scudetto triumph since 2009-2010 this season with four games to spare and is under contract for another year.
However, the Italian giant is facing well-documented financial issues and Conte is reportedly considering his future beyond the end of this campaign.
Talks are said to be planned between the ex-Chelsea boss and president Steven Zhang once Inter has played its remaining two league matches.
And when asked whether Conte will still be in the Inter dugout next season, Marotta could not give a definitive answer.
"As a person and a director, I certainly hope so," Marotta said. "He helped to start a new era in two seasons that were affected by COVID.
"If we look over two years of the Conte era, we have second place in Serie A and the title won several weeks in advance, and have also reached the Europa League final.
"We certainly hope to continue together even during these difficulties."
Inter have asked players to accept a pay cut as part of a cost-cutting exercise, while the likes of Romelu Lukaku and Lautaro Martinez have been linked with moves away.
But Marotta insists the pre-existing contracts already in place will be respected by Inter should the players reject the club's request.
"Everything started with a meeting with the president, who explained the current moment football is experiencing with maximum serenity," he said.
"Zhang made the players aware of the delicate position the club is in, but he didn't oblige anyone [to take wage cuts]. It's up to everyone to make a decision with their conscience.
"We have full respect for the players who have given the club an extraordinary joy this season. I'll repeat: Inter will honour all their agreements."
Marotta was speaking ahead of Inter's meeting with Roma on Wednesday, which the Nerazzurri won 3-1 to make it a club-record extending 15 home league victories in a row.
Henrikh Mkhitaryan pulled a goal back for Roma after midfield pair Marcelo Brozovic and Matias Vecino had given Inter a two-goal advantage in a lively first half at San Siro.
But Lukaku's 22nd Serie A goal of the campaign - only Juventus forward Cristiano Ronaldo with 28 has more - tapped in late on to seal a first home win against Roma since 2015.
With that goal, Lukaku became the fourth Inter player to score at least 15 goals at home in a single Serie A season in the last 45 years, after Christian Vieri (19 in 2002-03), Diego Milito (17 in 2011-12) and Mauro Icardi (16 in 2016-17 and in 2017-18).
The game was a milestone occasion for Conte, who was taking charge of his 100th Inter match in all competitions since arriving at the start of last season.
He has won 63 of those games, which is the most of any coach in their first 100 games with the Nerazzurri since 1929-30.
Conte did not speak to reporters before or after the game, but assistant Cristian Stellini praised his players for their attitude to see off Roma with the Scudetto already sealed.
"It's always good when you play with this desire and fighting spirit," he said at the post-match news conference.
"There was a little tension, but we managed to make it 15 wins in a row at San Siro.
"Nothing changes after winning the title. You have to continue with the same mentality and attitude, although we can play with a little more happiness."
One blemish for Inter was losing Alexis Sanchez to an apparent ankle sprain before half-time, but Stellini is expecting the forward to make a swift return to action in time for the weekend trip to Juventus.
"He took a blow to his ankle and lost a bit of sensitivity, so he wanted to come off," the Inter assistant said. "We think we can get him back for the next match in Turin."