Spurs boss Mauricio Pochettino is keen to bolster his attack before the end of the summer transfer window, with Emmanuel Adebayor and Roberto Soldado reportedly on the way out of White Hart Lane.
According to London Evening Standard, Spurs are currently in talks with West Bromwich Albion over Berahino while the London club believes its a good chance of signing Hernandez.
West Ham United are also keen on making a move for Hernandez, and the Daily Star on Monday reported that the Hammers are lining up a £12m bid for the Mexican international.
Manchester United may not be keen to strengthen one of its rivals by selling the 27-year-old to Spurs, putting the move in jeopardy.
Tottenham reportedly made an enquiry over a £15m deal for Berahino, however West Brom value the player at £20m.
The Baggies completed the £12m signing of Zenit St Petersburg attacker Salomon Rondon on Monday, meaning Tony Pulis could now be ready to allow Berahino to leave The Hawthorns.
Berahino has also been linked with a move to Arsenal, but it seems Tottenham are in pole position to sign he England Under-21 international.