Mane instead moved to Anfield following two seasons at Southampton, and he's been a big hit with the Merseyside club.
The Senegal international has said that there was serious interest from Old Trafford, though, revealing in an interview with South African television network SuperSport (h/t Chris Burton of Goal) that he spoke to then-manager Louis van Gaal about a possible switch.
"Some teams wanted me—Manchester (United), the wrong team wanted me," Mane said. "Of course, I spoke with Van Gaal, and they even made an offer. But for me it was not the right club, it was not the right moment. To feel this—the right moment, the right coach, the right club."
Mane also said that Liverpool manager Jurgen Klopp had previously tried to sign him in 2014 when the player was at Red Bull Salzburg and the coach was in charge of Borussia Dortmund.
Here's a look at what else he had to say in the interview:
Eventually, the pair linked up at Anfield, and together they've made rapid progress. Mane has developed from an inconsistent winger into one of the most devastating forwards in the Premier League.
The Senegalese has been potent in his two seasons for the Reds, and late last term and early in this one, he's been in exceptional form for Liverpool:
Mane quickly became the team's key attacker in his first season, and the Reds did look a little one-dimensional in their forward play when he was absent.
However, in the previous campaign, the former Southampton man linked up with Roberto Firmino and Mohamed Salah. The trio struck up an incredible understanding, with Mane's blistering pace and direct running giving defenders many issues from the left flank.
The Senegal star has also developed a reputation for netting in big games. Mane scored in every round of the knockout stages for the Reds as they made their way to the UEFA Champions League last season, including an equaliser in the final before Liverpool went on to lose 3-1.
After Mane's goal in the recent 2-0 Premier League win for Liverpool away at Crystal Palace, Klopp outlined why Liverpool were so intent on getting him:
While it would be easy to say Mane would have been a huge success at United, under Van Gaal and potentially current boss Jose Mourinho, the player wouldn't have been given the attacking freedom he has under Klopp. The coach's high-intensity football suits Mane perfectly, too.
Liverpool supporters will be delighted with their new No. 10, although they will be hoping he can step up another level in the coming campaign. If he does, then the Reds will be in an excellent position to challenge for major prizes.