Spurs have made just two signings this summer in Netherlands international Vincent Janssen and former Southampton midfielder Victor Wanyama. The club are expected to conclude deals for Espanyol goalkeeper Pau Lopez and Marseille winger Georges-Kevin Nkoudou, but Pochettino is also keen on a player who can play in "the second line of offence".
Wilfried Zaha was thought to have been the club's first choice, only for Crystal Palace to swiftly turn away their initial offer of £12m ($15.7m, €14m).
Speaking after his side's 1-1 draw with Liverpool on Saturday, the Argentine coach highlighted Mane as the sort of player he needs to complement his current options in attack.
"We need a player that is more direct, a player that is more aggressive and offensive," Pochettino said, the Liverpool Echo report. "We have a player like Eriksen or Son or Lamela that are players who like to play into feet.
"Some characteristics like that we see today from Liverpool. Mane, this type of player that can be offensive."
According to the Guardian, Tottenham have returned with a bid of £21m for Zaha. Steve Parish, Palace's chairman, insisted however last week any future bids for the former Manchester United winger would be swiftly rejected.
"We had a bid from Spurs but £12m – it's ridiculous. I can't imagine that they're serious," Parish told talkSPORT.
"There is no chance whatsoever of Wilfried Zaha leaving the club in this transfer window. I can absolutely reassure every Palace fan he is an integral part of our plans. We've told Spurs that there is really no point bidding for him because he is going nowhere - 100% guaranteed."