The 22-year-old has been linked with a move to AC Milan after club president Silvio Berlusconi highlighted him as one of a number of players he is looking at to form a new, younger team at the San Siro.
Santon has made 52 appearances for Newcastle following a £5m move from Inter Milan in August 2011.
Roma were linked to him all summer, but Derek Llambias was quick to point out: "We heard the rumours, but no club asked about him, and there certainly was no offer."
Davide Santon: "I have had a year and a half here. I really enjoy it. I am happy at the club.
"This is really important for a young player. We are a young team here and we are growing together.
"That will only make us stronger in the long-term.
"The team give me confidence to play my game.
"If you play when you are stressed you can't give 100 per cent. But when you are settled as a group you can do well.
"I know I can do better than now, though.
"And when we have all of our players fit, we know we can do better as a team."