While Messi has spent his entire professional career at Camp Nou, the Argentine was linked with a switch to San Siro earlier in the year.
However, Branca has revealed that Inter already have history regarding Messi, hinting that the legendary attacker was not interested in taking a pay rise at the Italian giants.
Speaking to Libero, Branca said: "Yes, we moved for him but Leo did not want to leave Barcelona. He was very grateful to the club. Money does not always come first."
At the time, Messi was just 21 years of age and had not scored more than 17 goals in a season.