Horta, 25, has been identified by Leipzig as an alternative to Werder Bremen attacker Milot Rashica.
Talks for Rashica have stalled because the two clubs are so far apart on their valuations.
Leipzig are now looking to Horta, regarded as one of the best talents in Portugal’s top flight.
Horta scored 24 goals for Braga last season, including strikes against Wolves and Besiktas in the Europa League.
He has been capped once by Portugal back in 2014 and a move to Leipzig could improve his national team chances.