According to The Sun, the Paris and Catalonia clubs have made contact with Coutinho's representatives and value the playmaker at £25 million, a figure that is expected to rise as the bidding war commences.
However, the move could prove to be slightly premature, as the Brazilian still seems to be in a growing phase, with a few areas of play that need to be polished.
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Although a transfer to PSG or Barca might seem mouth-watering on the surface, such a big move at the wrong time could dent a blossoming career.
More Opportunities to Develop at Liverpool
The 23-year-old is a firm favorite at Anfield and has been exciting the crowd with his dazzling displays from midfield ever since his arrival from Inter Milan in 2013.
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Having been nominated for the PFA Player of the Year, as well as the Young Player of the Year in 2015, the playmaker definitely has the potential to become one of the best players in the Premier League, if not the best.
Not many players of Coutinho's creative style and ability are able to express themselves freely in England's top flight, making him a unique talent.
Despite Coutinho's ability to link well with attackers, the Brazilian often fails to deliver in the final third, either making the wrong decision or being over-powered by defenders.
That is an aspect the midfielder needs to improve upon and under manager Jurgen Klopp, Coutinho has the perfect opportunity to do so.
The midfielder's lack of strength is yet another aspect that needs improvement.
As a first-team regular at Liverpool, playing over 30 games per season, the midfielder will have the chance to refine his game play further.
Possible Lack of Action at PSG or Barca
PSG already have a strong contingency of attacking players in the team. Players such as Javier Pastore, Lucas Moura and Angel di Maria are established players at the Parc des Princes, leaving little room for another attacking midfielder to slot into the side.
Unless one or two of the above players decide to leave, Coutinho would be up for some serious competition in Paris.
The 23-year-old would also face competition for a place in the midfield three with Marco Verratti, Blaise Matuidi and Thiago Motta serving as a reliable trio.
Also, considering the financial power of PSG, more players are bound to arrive at the club making it even harder for Coutinho to fit into the first team.
Brazilian teammate Neymar stated his desire to play with Coutinho and would welcome the midfielder with open arms at Barcelona.
However, the Brazilian forward also expressed that the Liverpool midfielder might have to settle for a place on the bench initially, potentially serving as a backup to 'MSN'; the trio of Lionel Messi, Luis Suarez, and Neymar, and rightly so.
Similar to PSG, Barca also adopt a triangle of players in midfield with Ivan Rakitic, Sergio Busquets and Andres Iniesta being the current preferred three, again making it tricky for Coutinho to feature in the first eleven.
There are, however, a few plus sides to joining the above two clubs, one of them being Champions League football. Secondly, these teams are perennial title contenders in their respective leagues and have the ability to truly challenge for the Champions League trophy as well.
Also, Coutinho would likely receive a massive increase in weekly wages if he ends up in any of the above clubs.
Despite all the great perks that come with playing for a European giant, the likelihood of Coutinho spending a fair share of his time on the bench is high, which would be an undesirable hindrance to the midfielder's development.
There is no reason to rule out a possible big move in the future, but a move as early as this summer could derail the Brazilian's surge towards becoming a fully developed player.
Should Philippe Coutinho stay at Liverpool this summer? Let us know YOUR thoughts in the comment section below!