Defender Skriniar has been a standout performer for Luciano Spalletti's side since joining Inter from Sampdoria prior to the 2017-18 season.
The 24-year-old's performances have seen him linked with a move to a host of major clubs across Europe, but Skriniar has now confirmed that talks to remain at Inter are nearing a positive conclusion, insisting he is unaware of how the transfer rumours came about.
While reportedly a target for the likes of Manchester United, Barcelona and Real Madrid, the centre-back is only interested in helping his current team qualify for next season's Champions League, starting with a win over Udinese on Saturday.
"Very little," Skriniar, whose current contract runs through the summer of 2022, told DAZN when asked what stood in the way of him agreeing a new deal with Inter.
"I believe my future is here. I don't know where this thing about Real Madrid came from.
"If we win three games we're there [in the Champions League]. We must win in Udinese. It's a difficult match because they have something important to play for, but it also is for us. We must win there."
Reports have surfaced in Italy that Skriniar could be named Inter captain for next season, taking over from current incumbent Samir Handanovic, who replaced Mauro Icardi in the role in February.
Skriniar, however, says getting the armband would not change his approach, noting a player's effort level should be the same regardless of the captaincy.
"I don't think about the captain's armband. I just think about playing. Nothing necessarily changes with it," Skriniar added.
"You gain extra responsibility, but even if you don't have it you always have to give everything on the field and fight."
Skriniar and Inter are in a battle to make the top-four in Serie A and sit in third on 62 points with just four league games remaining.