Spanish journalist Gerard Romero, who has good connections to Barcelona, reports Newcastle are again moving for Torres.
The Toon have made a bid of €15 million (£12.6m) plus €5 million (£4.2m) in bonuses.
It is unlikely that Barcelona will accept such a low bid considering what they paid for Torres.
The striker has scored 25 goals and 13 assists in a total of 113 competitive matches for Barcelona.
Torres has a contract that runs until the summer of 2027.