Barca, who paid upwards of £100m to sign the Frenchman from the Madrid outfit in 2019, are said to have been keen to offload the 30-year-old throughout the summer, as they battle through financial difficulties.
After joining from Real Sociedad in 2014, Griezmann hit 94 goals in 180 appearances for Los Colchoneros, before they received their record fee for a departing player, taking the forward to the Camp Nou.
Since his arrival in Catalonia, the World Cup winner has made 74 appearances for the Blaugrana, netting 22 goals and adding Copa del Rey title to his trophy cabinet in that time.
While rumours have arisen around a swap deal for Joao Felix, who arrived at the Estadio Wanda Metropolitano after the departure of Griezmann, the clubs are now close to agreeing a loan deal with an option to buy, according to Florent Torchut.
Such a move would see Griezmann return to Diego Simeone's side after they triumphed in La Liga last season, breaking a seven-year wait for the top-flight title.