That's according to the Daily Mirror, which claims that chief executive Ivan Gazidis insisted on the clause as the club drove a hard bargain with the European champions.
And if we do not buy him back, we will get 50 per cent of any fee if Barcelona sell Fabregas elsewhere, it is reported. The paper adds that it leaves Arsenal believing that months of haggling have paid off - and that it is a better deal than Barca are suggesting.
However, AW himself has admitted the Catalans got Cesc on the cheap. He said: "We sold Cesc for a reduced fee. If you can make an auction between Real Madrid, Chelsea and Manchester City, you will certainly get more money, but he just wanted to go to Barcelona.
"Cesc went because he was desperate to play for his home town at a club where his grandfather was a member of the committee. It's not a financial affair but one of the heart."
AW added in the Sun: "Yes, we lost a world-class player and we are sad about it. We did fight to keep him but in the end we have to respect the player's desire. This club is 125 years old and many big players have left. We want to show we have strength and unity to fight as we always do."
Arsenal face a crucial CL game tonight against Udinese at the Ems and AW has called for the disgruntled fans to back the team. He told the Telegraph: "I understand everybody's worry but I believe as well a club is a united front. Our players need the support from our fans. We have not to forget that the most important thing to keep your best players is that they have love from the fans and everybody inside the club.
"Our fans can be proud of the way we run this club, of the quality of player we have and of the financial situation that is existing at the club. Rather than convicting this club, they have more reason to be proud. It is an important period for this club, but I am confident we will get over it in a very successful way. We need to remain united."
AW has given the biggest hint yet that he won't be spending money on new recruits despite Cesc going and Nasri on his way. He added: "I don't think just spending money is a target that is defendable. We are not frightened to spend money, but we have to be convinced the player is better than what we have.
"Everybody says to me: 'Buy'. But when I say 'who?' there is a no-man's land. We will try but let's not forget that we have brought players in. They are all quality. If you watched our two centre-backs on Saturday, I'm not convinced we have a lack of quality there. We have Ramsey, Wilshere and upcoming players who have to take responsibility."
Decent bit of banter from AW over Nik Bendtner, who could play tonight. The striker has already insisted publicly he wants to leave Arsenal, and Sporting Lisbon, Borussia Dortmund, Newcastle and Sunderland have all shown interest.
But Bendtner has yet to find himself a new club and - despite missing all of Arsenal's pre-season friendlies - is in the squad for the first leg of their Champions League qualifying tie against Udinese. Robin van Persie's suspension and Marouane Chamakh's lack of form look like combining to produce a remarkable return for Bendtner, who trained with the first team on Monday.
Arsenal boss Arsene Wenger claimed the Dane could even stay at the club, despite Bendtner going on TV last week to plead for a move. AW told the Mirror: "In his interview Bendtner, said he was gone. But I checked, and he's not gone at all! I promised I'd let him go if he found the right club and that hasn't changed. When I make a promise, I keep it.
"But if he doesn't find the right opportunity, he'll stay and fight for his place like everybody else. He looks sharp in training."
CARL ELDRIDGE - Follow me on Twitter @eldomedia