The paper claims Messi demanded that Barca insert a release clause in his latest contract, signed late previous year, which stipulates that he will only stay at the club in the event of independence if they remain in "a top European league".
The Catalans are still unbeaten in La Liga this season and have Philippe Coutinho to come in, with the Brazilian expected to be officially unveiled as a Barcelona player on Monday following the announcement of his 160 million-euro ($192 million) move from Liverpool.
And Suarez's strike was also a milestone goal, a powerful volley before half-time his 132nd for the club, moving him above Samuel Eto'o to become Barca's seventh-most prolific goalscorer.
Barca relaxed a little after the break, but Brazilian worldwide Paulinho added an extra shine to the win by tapping in as the game drew to a close.
It was Messi who broke the deadlock from a Jordi Alba assist, a combination that has proved fruitful on so many occasions this season.
In the 38 minute Barcelona did find their second goal when Luis Suarez latched onto an inch-perfect cross from Sergi Roberto just outside the box and arrowed the ball into the top left corner, 2-0.
With Barca surprisingly sloppy in possession and open at the back, Jason set up Shaquell Moore for a fine chance but Ter Stegen saved again to maintain his fourth consecutive clean sheet of the campaign.
Barcelona reserve-team striker Jose Arnaiz debuted in the league as a late substitute.
Lionel Messi and Luis Suarez each scored in a routine if underwhelming win at home to struggling Levante, with Paulinho increasing their lead in added time.