The Senegal international was the last of the Reds’ fearsome attacking unit to commit to fresh terms at Anfield.
Roberto Firmino and Mohamed Salah had led the way, but Mane only put pen to paper in November 2018.
He was said to be attracting interest from afar before that deal was done, with Madrid mooted as one possible landing spot, but Mane insists he never considered a move away from Merseyside.
The 26-year-old forward, who is now tied to Liverpool until 2023, told World Soccer: “Speculation is part of football. You just learn to live with it and not to take it too seriously.
“All I can say is that my only concern is Liverpool. Mo, Bobby... it seemed like everyone was signing contracts and they were saying: 'Hey Sadio, when are you going to sign?'. I said to each of them: 'Don't worry bro, I will sign'.
“And what did I do? I signed... so they are pleased now!
“I'm very happy here and I think people are happy with me too. We want to write our names alongside the many great ones in the story of this club. Hopefully it's the beginning of something special.”
Mane has starred for Liverpool since being snapped up from Southampton for £34 million ($45m) in the summer of 2016.
He has netted 43 goals in 101 appearances, with nine of those efforts recorded in the Premier League this season to help the Reds to the top of the table.
There is a determination on his part to help Jurgen Klopp’s side to major silverware, with Mane adding: “I can't wait to lift a trophy with Liverpool. I know the fans are desperate for us to win the Premier League.
“It would be an amazing moment for the club. It has been far too long for a team the size of Liverpool.
“We believe we are heading in the right direction, but there are some very tough rivals – City were unbelievable last season and very strong again – but why not?”
Mane, Salah and Firmino will be expected to help maintain Liverpool’s title challenge in 2019, with the trio having netted 131 times between them over the course of the last 18 months.
“I think it just happened naturally,” Mane said of a productive partnership with two other star turns.
“When you have players like Bobby and Mo they just make everything easier.
“We just seem to instinctively know each other's movement and I think you can see that we enjoy playing together. We want to get even better and score even more goals. Our best is still to come.”
Liverpool, who are four points clear at the summit, are back in action on Wednesday when Leicester pay a visit to Anfield.