When making the shock switch from Barcelona to Parc des Princes last summer, the legendary forward was handed a two-year deal.
However, with the 35-year-old having been strongly linked with a stint in the MLS before the end of his career, it remains unclear whether the player would be open to extending his time in France's capital.
According to Marca, the Argentine will be given the opportunity to commit to a longer period at the Ligue 1 champions.
The move comes after PSG decided to make significant changes to their coaching and transfer setup with Christophe Galtier and Luis Campos having recently moved to Paris.
PSG are seemingly keen to build for both the short and long term, which includes trying to keep Messi at the club for a third season.
While the report adds that a formal contract proposal has not been presented to his representatives, there is said to be a desire to hold discussions.
However, Messi and his camp are reportedly not prepared to make any decisions with regards to his future before the World Cup, which will start in November.
Despite helping PSG win another Ligue 1 title last season, Messi endured somewhat of an indifferent campaign in his new surroundings.
Although he contributed an impressive 15 assists, Messi netted just six times in 26 league appearances, his worst return since 2005-06.
Five strikes came from seven outings in the Champions League, but PSG bowed out at the last-16 stage after a dramatic collapse against eventual winners Real Madrid.
While backup to Kylian Mbappe is expected to be signed at some stage this summer, no player will be brought to the club which will challenge Messi's place in the team.
Galtier and Campos are instead focused on bringing in defenders and midfielders with Milan Skriniar being tipped to join Vitinha in making the switch to Les Parisiens.