Cesc Fabregas left Barcelona for Arsenal in 2003. REUTERS

Barcelona are set to make their second offer of the summer for Arsenal captain Cesc Fabregas, with an improved bid of around €40 million (£35 million), reports suggest.

Arsenal have already rejected a £27m offer for their captain but the European champions will make one final attempt to conclude their three-year pursuit of the Spain international.

Negotiations between the two clubs are on-going as Barcelona continue their pre-season tour of the U.S., with manager Pep Guardiola clarifying he views Fabregas as the missing link in his current squad.

Guardiola told the Daily Telegraph: "We're short of just one player and everyone knows which one that is."

But manager Arsene Wenger remains adamant Fabregas will not be sold for less than £40m and it is far from certain the club will accept any new offer from Barcelona that falls short of their valuation.

Nevertheless, any further developments are likely to remain behind closed doors until a conclusion to one of football's longest running transfer sagas is resolved.

Barcelona director of sport Andoni Zubizarreta told reporters earlier, "Negotiations shouldn't be live broadcasted. You have to show respect. We won't comment on the Fabregas talks now."

Fabregas has missed all of Arsenal's pre-season matches this summer, with reports blaming a recurrent hamstring injury as well as the 24-year-old's "unsettled" mental state.

Wenger faces a further headache tomorrow at the club's annual member's day. Next season's team photograph is scheduled for Thursday and the club are believed to be considering taking two photos - with and without Fabregas - to avoid any embarrassment if the midfielder is subsequently sold to Barcelona.