Argentine media reported on Thursday that Suarez arrived on a private flight from Montevideo, accompanied by his partner Sofia Balbi and their children.
He and Messi became close friends when they played together for Spanish club Barcelona.
More than five million people took to the streets of Buenos Aires to congratulate "la Scaloneta" on Tuesday but with the city overflowing, the players had to be airlifted out by helicopter before Messi and Angel Di Maria (34) travelled to Rosario.
The Argentina captain is staying in his home at the Kentucky Country Club and local media reported that many international sports stars are due to join the celebrations, including former Spain midfielder Andres Iniesta and former Argentina striker Sergio Aguero (36).
