Despite comfortably leading PSG to the Ligue 1 title with four games to spare in 2021-22, Pochettino is still widely expected to depart the club before next season.
The Argentine saw his side's Coupe de France defence ended by Nice in the last-16, while they collapsed during the same stage against Real Madrid in the Champions League.
Pochettino's contract at the Parc des Princes now has less than 18 months left to run, and the PSG hierarchy are rumoured to be scoping out a shortlist of candidates.
Zinedine Zidane was the original favourite to take the reins, but the ex-Real Madrid coach supposedly has no interest in returning to the French capital.
According to Le Parisien - via Get French Football News - Sporting head coach Amorim is now the priority target for PSG and incoming sporting director Luis Campos.
As well as Pochettino, Leonardo is also expected to move on in the summer, and Les Parisiens are understood to be closing in on the appointment of Campos, who left Lille in 2020.
After retiring as a player in 2017, 37-year-old Amorim enjoyed short stints in the Casa Pia and Braga hotseats before taking charge of Sporting in March 2020.
Amorim had already won the Taca da Liga with Braga, and he achieved the league and cup double with Sporting Lisbon during a phenomenal 2020-21 campaign.
The Green and Whites won 26 and lost just one of their 34 league games under Amorim's tutelage last year to finish five points clear of Porto, but they could not defend their title this time around.
However, the former Portugal international still won the Taca da Liga and Portuguese Super Cup in 2021, as well as reaching the semi-finals of the Taca de Portugal and qualifying for the Champions League knockout stages.
In total, Amorim has won 77, drawn 15 and lost 14 of his 106 games in charge of Sporting, and his contract with the Portuguese giants does not expire until 2024.
Following the extension of Kylian Mbappe's contract at PSG, Pochettino has confirmed that he plans to hold talks with Nasser Al-Khelaifi over his future at the club.
"The club will do what they see fit, like last summer. For the moment I am still the coach, and I will also take part in that decision," Pochettino told the press, as quoted by Marca.
"Without a doubt, I should see the president in Qatar. I'm sure we will see each other. But to be clear, the planning of our meetings is always done by our superiors."
Pochettino's 84 games in charge of PSG have brought him 56 wins, 13 draws and 15 losses, and there has been speculation over a possible return to Tottenham Hotspur while Antonio Conte's future remains up in the air.