The Brazil international sealed his dream transfer to the Nou Camp from Liverpool last January in a deal worth £142m.
But despite a promising start, Coutinho has struggled for form this season and is no longer a regular starter under Ernesto Valverde.
Reports have suggested the playmaker is unhappy in Spain and is desperate for a move.
United have been linked with an approach, as have former club Liverpool.
And according to Goal, Barca are prepared to listen to offers for the 26-year-old.
The report claims the Catalan club will consider selling Coutinho for around €80m (£68.8m), a considerable loss on what they paid.
The revelation will have put United on red alert as they prepare their summer transfer plans.
Coutinho’s availability comes amid news that:
“I think it would be difficult to prise players away from the club now.”
Liverpool legend Jamie Carragher
However, according to Goal, Coutinho is not interested in a return to the Premier League.
The report claims his family struggled to adapt to life in England, ruling out a move to United or Liverpool.
And it appears a switch to PSG seems most likely, which would see him reunited with international team-mate Neymar.
Liverpool will be desperate not to lose any of their stars this summer, with Real Madrid expected to splash out under new boss Zinedine Zidane.
But Reds hero Jamie Carragher believes Jurgen Klopp can convince his stars to stay put.
“Liverpool did lose Philippe Coutinho not so long ago but I think it would be difficult to prise players away from the club now,” he told Sky Sports.
“Of course if Real Madrid and Barcelona come calling for your players, it’s very difficult, because most players anywhere want to play for those two clubs.
“But I think right now the players absolutely adore Jurgen Klopp and they want to stay part of this journey.”