The 27-year-old's long-term future at San Siro is believed to be uncertain as his current contract is due to expire next summer.
Paris Saint-Germain were understood to have made an offer in the region of €70m (£60.5m) for Skriniar over the summer, but a move for the centre-back to the French capital failed to materialise.
Premier League quartet Chelsea, Manchester City, Manchester United and Tottenham Hotspur have also been credited with an interest in the Slovakia international.
A recent report claims that Inter could sell Skriniar for as little as £10m in the January transfer window if he decides against extending his contract.
However, Marotta has suggested that the is still a chance Skriniar will commit his future to the Nerazzurri, but the final decision is set to be made by the defender himself.
"We are confident, even if we know that a great deal here depends on what he intends to do," Marotta told Sky Sport Italia via Football Italia.
"We will soon discuss the situation with him, as far as we are concerned, we want to reach an agreement. We are dealing with a serious professional who loves Inter."
Marotta has also responded to claims from the Financial Times that Inter's owners Suning are looking to sell the club and have linked up with Raine Group - who played a key role in the sale of Chelsea earlier this year - to begin the search for potential successors.
"It is a situation that is above my head, so I can only say that the owners are very close to the team and always fulfilled their financial obligations," Marotta added.
"We are a club who keep up our payments, and over the years of their tenure, the Zhang family invested hundreds of millions of Euros into this club."
Skriniar signed for Inter from fellow Serie A side Sampdoria in the summer of 2017 and he has since made 229 appearances for the Italian giants in all competitions.
During his time at San Siro, the 54-cap Slovakia international has won the Serie A title, Coppa Italia and the Supercoppa Italiana, and he was also a Europa League runner-up in 2019-20.
Should Skriniar fail to agree terms with Inter over a contract extension before the New Year, the defender will be able to negotiate pre-contract agreements with foreign clubs over a free transfer in the summer.
Skriniar is not the only Inter player who is out of contract next summer, as Stefan de Vrij, Edin Dzeko, Matteo Darmian, Samir Handanovic, Danilo D'Ambrosio, Roberto Gagliardini, Dalbert and Alex Cordaz will also see their current deals expire in June 2023.