Salah, 32, has defied the distraction of months of speculation over his future by scoring 27 goals and providing 17 assists in the 31 league appearances to help open up an 11-point lead at the top of the table with seven games to go.
The Egyptian was part of the Liverpool side that delivered the club's first league title for 30 years in the 2019/20 season.
But Covid restrictions meant that the Reds lifted the trophy in front of an empty Anfield and there was no parade through the city's streets.
"I think I said in the beginning of the season, I just want to win the Premier League more than anything else. I want it so bad," Salah told Liverpool's website.
"I think we owe that to the fans. They deserve it, they deserve to enjoy it after that long time, with celebrating at Anfield and in the street and just enjoying ourselves winning the Premier League."
He added on the prospect of winning the title in front of a full Anfield: "That's something that drives me crazy every day –- to come to work and push myself and push the other players also, because we are closer than ever now that we can win it in a special way."
Liverpool manager Arne Slot has also had to deal with persistent questioning over the futures of captain Virgil van Dijk and right-back Trent Alexander-Arnold, who are also out of contract at the end of the campaign, during his first season in charge.
The Dutchman said news of Salah's new deal may have come as a "pleasant surprise" for supporters but praised the club's sporting director Richard Hughes for ensuring the Egyptian remains at Anfield.
"I don't think it's a surprise to you that I knew a bit better how his contract situation went over the course of the whole season," Slot told a press conference ahead of Sunday's Premier League home game against West Ham United.
"Maybe for the fans it was a pleasant surprise. I knew it a bit longer, of course, that things were heading in the right direction.
"I think it's also a big compliment for Richard that he achieved to extend Mo Salah, who is such a great player as a free agent, that he can go probably to every club in the world wherever he wants to. But he stayed at our club and that's also a compliment for Richard."
While fans were thrilled by the news, anticipation is building over Liverpool captain Van Dijk and Alexander-Arnold, who has been linked with Real Madrid.
"If you want to sign players or keep players, it is always a positive one of our star players has made the choice to extend," Slot said.
"In general people see me as relaxed and that has all to do with the trust I have in the quality of the players and the quality of leadership in (club owners) FSG. That is why I am indeed calm.
"They will do what is best for the club. If that is extending then it is, if not, they will find a solution.
"I have also spoken to Mo and followed the process. It gave me confidence. Sorting them before the end of the season would be useful."
Slot added that Salah's decision proved that the Egyptian believes the club can compete for more trophies as they close in on the Premier League title this season with an 11-point lead at the top of the standings.
"He has always been judged as a player, but I also see him as a human being and he is humble, works hard and puts so much effort into becoming the player he is. He keeps up that effort every single day," Slot said.
"Salah can score goals if he is not in the best half hour or 15 minutes and that is why he is mentally so strong. He has to be strong mentally and apart from the other things that is probably what stands out for me...
"What it might tell you is that it is not only a good season now, we want more next season and Mo is convinced we can do so. So that is positive for us."
Slot confirmed goalkeeper Alisson Becker is available for Sunday's game after undergoing concussion protocols after suffering a head injury while on international duty with Brazil.