The Daily Mail claim the French champions are considering meeting the £153m release clause in the Brazilian's contract.
If they chose to do so and were able to complete a deal, it would be the blockbuster transfer of the summer and a new world-record for money spent on a single player.
PSG are looking to replace Ibrahimovic who will not renew his contract in Paris.
The enigmatic Sweden striker - currently preparing for Euro 2016 - is
reportedly close to agreeing a deal with Manchester United and
reuniting with Jose Mourinho.
Neymar's contract runs until 2018 but Barcelona could apparently be tempted to do business if the release clause is met.
The 24-year-old was in sensational form for the Spanish champions
this season, scoring 31 goals and providing 27 assists in all
competitions.
His partnership with Lionel Messi and Luis Suarez helped the Catalan
club to domination on the domestic front and a Club World Cup win.
United have been touted with interest in Neymar in the past but with
the apparent arrival of Ibrahimovic, PSG would be in the driving seat to
sign the Brazilian.
