The 56-year-old made the shock announcement in January that he would be leaving his role as Liverpool manager at the end of the season.
Klopp oversaw Liverpool's recent success in the EFL Cup final against Chelsea, and he will be determined to collect more silverware before he bids farewell to the Merseyside club.
While Klopp is currently focused on matters on the pitch, the Liverpool hierarchy are preparing the club for life after the German's departure.
Bayer Leverkusen boss Xabi Alonso has emerged as the frontrunner to succeed Klopp at Anfield after impressing during his time in Germany.
Alonso has helped Leverkusen establish a 10-point gap at the top of the Bundesliga table, while he has also led the club to the DFB-Pokal semi-finals and the last 16 of the Europa League.
Although Liverpool have supposedly made an initial approach for Alonso, they are expected to face competition in their quest to secure his signature.
German giants Bayern Munich have pinpointed Alonso as a potential successor to Thomas Tuchel, while Leverkusen are still determined to retain the Spaniard's services.
As a result, Liverpool are believed to be considering a number of alternatives, including the current Sporting boss Amorim.
According to The Mirror, the Reds have sent officials to watch Sporting in action as they carry out due diligence on the 39-year-old manager.
The report claims that club representatives were in attendance at the Estadio Jose Avalade for the first leg of the Taca de Liga semi-final tie with Benfica.
Goals from Pedro Goncalves and Viktor Gyokeres proved enough to seal a 2-1 victory,
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