Express Sport understands the Reds have set their sights on the Senegal international after missing out on Bayern Munich midfielder Mario Gotze.
Mane would become the fifth Saints player in the last two years to join Liverpool, following Adam Lallana, Dejan Lovren, Nathaniel Clyne and Rickie Lambert.
The Blues supporter initially wanted to join the Stamford Bridge club after informing Southampton of his decision to leave, but Mourinho reportedly didn't make a good impression.
The England international instead opted for a £30m move to Old Trafford, where he put pen to paper on a four-year deal.
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Luke Shaw reportedly rejected Chelsea move after talks with Jose Mourinho
Estadio Deportivo claim the 26-year-old is calm over his future and will not actively seek an exit from the Europa League champions.
United have been linked with a big-money move for the Poland international, whose new deal in November included a £34m release clause.
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