Sources have told ESPN that Barca and City officials met in Seville on Tuesday to put the finishing touches to a deal that will be worth an initial €55m with a further €10m ($11m) in potential add-ons.
However, Barca still have work to do to pull off the transfer. They are hampered by LaLiga's financial restrictions and must move players on before they can make new signings.
Their spending limit for the season has been set at €97m ($110m) by the Spanish league, which is significantly lower than their wage bill but they are permitted to spend 25% of any savings they make, be that in wages or transfer fees.
Sergio Aguero's retirement has freed up some room but they still have much more work to do to be able to sign in January. The club are looking for new clubs for Neto, Samuel Umtiti and Philippe Coutinho, three players that are deemed surplus to requirements, but will also listen to offers for other players.
Sources first told ESPN in November that Barca had stepped up talks with City over a move for Torres, a player they have held a long-standing interest in.
New coach Xavi Hernandez quickly made it clear he wanted attacking reinforcements in January and Torres emerged as Barca's first target, with director of football Mateu Alemany travelling to Manchester to accelerate negotiations last month.
Barca's financial situation is now the only thing holding up the deal. The club's gross debt stands at over €1 billion ($1.13b) and Alemany recently said they are not able to register new players in January while adhering to LaLiga's salary cap.
Torres has scored 16 goals in 43 appearances for City and another 12 in just 22 caps for Spain.