The centre-back has three years left on his deal but is reported to have been negotiating a year-long extension that will include a pay rise.
Skriniar has shone at San Siro since arriving from Sampdoria in July 2017 and has been linked with Manchester United and Barcelona.
However, the Slovakia international insists he wants to stay in Milan.
"You all know I want to stay at Inter," the 23-year-old told Tuttosport.
"I have a great relationship with the club and the directors. We're talking and we're close to an agreement."
Skriniar has sought to distance himself from transfer talk on a regular basis over recent months.
Just last week he hit out at reports suggesting that he would look for a way out of Inter if the club brought in added competition at centre-half.
He insists that is not the case and is hoping to soon have an experienced new team-mate alongside him, with Atletico Madrid's Diego Godin said to be interested in moving to Italy.
"Godin would bring experience and a winning mentality," he said. "He is someone who has won trophies. He can give us a big helping hand and help us to become stronger."
For now, Skriniar is focused on learning from the world's finest central defenders as he looks to cement his place among them.
"The strongest? Sergio Ramos," he replied when asked who the best in his position is. "Every year, he is voted among the best, he has won many Champions Leagues and he scores plenty of goals.
"I also like [Virgil] Van Dijk, I've watched a lot of David Luiz and Thiago Silva, because I want to take something from each of these champions."