"Arsenal captain Cesc Fabregas is under contract with the club until the summer of 2015," Arsenal said in a statement on Wednesday. "He is a highly valued member of the team and part of our future plans.
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"Yesterday evening we received an offer from Barcelona for Cesc and in response, we immediately and resolutely told them once again that we have no intention of selling our captain.
"To be clear, we will not make any kind of counter-proposal or enter into any discussion. Barcelona have publicly stated that they will respect our position and we expect that they will keep their word."
Barcelona revealed on Wednesday they had presented a firm offer to the London club the previous day.
"Everyone knows Cesc wants to play for Barca and everyone also knows we want to sign him but there is a third party that is Arsenal," director general Joan Oliver told the club's website.
Fabregas said last month he had spoken to manager Arsene Wenger about what he wanted and had left it in his hands.
The player came through the Barca youth ranks before moving to Arsenal at 16 but has never made any secret of his desire to return to the Catalan giants at some stage.
Fabregas is in Austria where Spain are preparing for the World Cup in South Africa which starts next week.
The 23-year-old is recovering from a cracked bone in his right leg but could return after two months out against South Korea in a warmup game in Innsbruck on Thursday.
Barca vice-president for sport Rafael Yuste said: "I am hoping we can sign him as soon as possible. I am optimistic and it's clear he, his family, the players and everyone else would give him a very warm welcome."
Fabregas would become La Liga champions Barca's second major signing in the space of a few weeks after they landed Spain striker David Villa from Valencia for 40 million euros last month.
