The paper claims Messi demanded that Barca insert a release clause in his latest contract, signed late a year ago, which stipulates that he will only stay at the club in the event of independence if they remain in "a top European league".
Barca, who have won 24 Liga titles and lead this season's standings by nine points, said after the referendum they would not speculate on the future.
Coutinho, who was denied a move to the Camp Nou last summer, is widely regarded as the heir to Andres Iniesta's throne and his arrival will only strengthen Barca's bid to reclaim La Liga.
With the win, Barcelona opened the gap between themselves and Real Madrid to seventeen points with our rivals playing Celta Vigo in their fixture later tonight.
The win took Barcelona's unbeaten streak to 27 straight matches.
Messi made his way back into the starting line-up after sitting out of Barcelona's draw with Celta Vigo in the Copa del Rey.
Until the deal for Coutinho, Dembele was the club's most expensive signing for a transfer fee of 105 million euros that could rise to 147 million euros.
Marking his 400th La Liga game in the most expected fashion, Messi scored a volley in the 12th minute of the game off Jordi Alba's cushioned header.
However, boss Valverde may be inclined to rest stars Messi and Suarez with tougher tasks ahead, while Mascherano has not featured for Barcelona since November 4.
Suarez struck his fifth goal in four games running by controlling a cross from Sergi Roberto and slamming the ball high into the net in the 38th minute.
Barcelona reserve-team striker Jose Arnaiz debuted in the league as a late substitute.