The German side have a limited budget this summer, which has caused them to miss out on Patrik Schick.
Schick, 24, is joining Bayer Leverkusen from Roma after impressing on loan at Leipzig last season.
Julian Nagelsmann turned to Sorloth as an alternative, but he too is considered too pricy for Leipzig.
According to BILD, Trabzonspor are demanding ‘well over’ €20m for a player they are paying €6m for.
Sorloth was on loan at the Turkish side from Crystal Palace last season and they will use their option to buy him.
The Norwegian had stunning 2019-20 campaign, which saw him score 33 goals in all competitions.
And as a result, his value has shot up and Trabzonspor want to spin a big profit if they are to sell him.
Vlahovic or Petkovic?
Leipzig are now looking at two strikers who are not at the top of their list, but would cost less.
Vlahovic, 20, scored six times in Serie A last season, including goals against Inter and Napoli.
The 25-year-old is also liked by Juventus and Roma and spent his entire professional career in Italy until moving to Zagreb in 2018.
Petkovic scored 13 goals last season for Zagreb and is ready for a move to a top European league.
In 2019, he became a regular in the Croatian national team, scoring five goals in his first eight games.