Coutinho has establisehd himself as a key member of the Reds side since signing from Inter Milan in January 2013, and the departures of Steven Gerrard, Raheem Sterling and Luis Suarez have seen the diminutive playmaker become a senior member of Brendan Rodgers' squad.
The Brazilian's performances in Red have seen him force his way into his national side following Dunga's re-appointment after last summer's World Cup, and his impressive form was rewarded with a new contract at Anfield back in February.
However, Neymar - speaking at a publicity event covered by ESPN - has said that he would love to see his compatriot join him at Camp Nou.
The Selecao skipper said: “Are there any Brazilians who could play at Barca? Many. I’d like Coutinho.”
Neymar's admission will be given short shrift by Liverpool fans who are tired of seeing their prized assets leave Anfield over the last few years.
Since 2009, the Reds have lost Xabi Alonso, Javier Mascherano, Fernando Torres, Luis Suarez and Raheem Sterling and there is a growing acceptance among the club's fanbase that they have become a selling club for Champions League heavyweights.
Along with perhaps a fully fit Daniel Sturridge, Coutinho represents a jewel in the crown that could be easily attainable for the likes of Barca should they wish to move for the talented Brazilian, and Neymar's words are unlikely to have gone down well in the corridors of power at Anfield.
Brendan Rodgers' men made a promising start to their campaign, with seven points taken from their first three Premier League games, but back-to-back reverses to West Ham United and Manchester United were followed up with a hugely frustrating 1-1 draw with Norwich City at Anfield on Sunday.
Rodgers' men can pick up their first win since they beat Bournemouth 1-0 back on August 17 when they entertain Carlisle in the League Cup on Wednesday.