Suarez is 33 in January and has received criticism from the Spanish media for showing signs of decline.
Barcelona are already searching for his replacement and have compiled a list of potential signings, according to Mundo Deportivo.
The Frenchman's PSG contract runs until 2022 and Barça are confident that if they can't do a deal next summer, they'll have a good chance in 2021.
It's believed that they are happy to wait in order to get their man, but if not they will turn to other targets.
Next on the list is Tottenham's talismanic striker Harry Kane, who has been rumoured to be frustrated in north London.
Kane's contract doesn't expire until 2024, meaning Spurs will command a huge sum of money for the England captain.
The 26-year-old already has seven goals in 10 games in all competitions this season, putting him on course for another high-scoring campaign.
Another name that appears on Barcelona's list of desirables is Manchester United's Marcus Rahsford.
Rashford was linked to the Blaugrana last summer, but the Spanish giants were thought to have baulked at his £100m price tag.
