Torres is being celebrated in Spain this week after his hat-trick in La Roja's 6-0 Nations League rout of Germany.
Cadena SER says before Valencia sold Torres to City over the summer, he was the subject of a formal offer from Barca.
The Catalans tabled a cash plus player proposal in January, with Barca starlet Monchu the player in question. But Valencia gave the proposal short shrift.
VCF would later sell Torres to City for €25m down plus €12m in bonuses.