Fabregas has long been linked with a return to Barca, the club where he plied his trade as a youngster before moving to the Gunners seven years ago.
The 23-year-old is under contract with the north London outfit until June 2014 but last month expressed his desire to head back to the Nou Camp at a promotional event in the Catalan capital.
That wish could have moved a step closer to reality over the past two days.
Barca director general Joan Oliver told the club's website: "Everyone knows that Cesc wants to play for this club and everyone knows that we also want this. But there is a third major player, which is Arsenal.
"Any deal must go through them and June 1 was the beginning of the period of official negotiations.
"Until earlier there were informal conversations, but since Tuesday these are formal - and the usual mechanism is to present a formal and concrete offer.
"So on Tuesday afternoon, we submitted a written bid to Arsenal."