Mane looks set to end his six-year stay at Anfield having not denied talk of an exit, the player even joking he'd follow the will of the Senegalese people and leave Liverpool.
The Reds have been linked with a number of players as they search for a replacement, including Leeds forward Raphinha.
Pulisic is another player Jurgen Klopp is interested in signing, German publication Bild reports.
It was widely reported Liverpool tried to sign the American before he joined Chelsea, however, the move didn't happen as Klopp was unable to provide Pulisic with first-team assurances.
There have been suggestions Liverpool could be interested in Pulisic's former Chelsea teammate Tammy Abraham, who was heard telling Trent Alexander-Arnold "I'm joining you next season" while training with England.
Bayern Munich appears to be the most likely destination for Mane, who has 120 goals for Liverpool.
His comments ahead of Senegal's Africa Cup of Nations qualifying clash against Benin, which saw Mane score a hat-trick, caused a storm.
Mane said: "Like everyone else, I'm on social media and I see the comments. Isn't it between 60 to 70 per cent of Senegalese that want me to leave Liverpool?
"I will do what they want. We will see soon! Don't be in a hurry because we'll see this together."
However, the player clarified his comments after the match, insisting they were meant as a joke.
Speaking to Canal+, Mane said: "I spoke yesterday while joking with a bit of humour and it was everywhere. I think we'll stop there.
"Liverpool is a club I respect a lot. The fans adopted me since day one. Regarding the future, we'll see."