Despite the Spaniard feeling he has a chance of running out at Wembley, Arsene Wenger is refusing to risk him on Sunday.
But Fabregas has been tipped to be fully fit for the Champions League showdown against Barcelona on March 8.
The Gunners talisman limped off in the 14th minute of Wednesday's 1-0 win over Stoke, and Arsenal manager Arsene Wenger said on Thursday night: 'It is a very small injury but Cesc will be out for Sunday. He is disappointed. We all feel sorry and sad for him. The only way we help him now is to win the Carling Cup as he contributed a lot in this competition.'
Early exit: Fabregas limped off in the the first half
Wenger refused to be drawn on whetherFabregas would travel to the Nou Camp for the Champions League second leg. But the Spain midfielder's personal trainer, Juan Ferrando, told a Spanish radio station last night the midfielder should play against the Catalan club.
He said: 'In principle, it is a microtear of the hamstring and he may play in the Nou Camp without problems.Without doubt.'
Wenger was willing to give Fabregas every chance to prove his fitness ahead of the Wembley clash against Birmingham on Sunday after tests on Thursday.
But with important games coming thick and fast especially that clash against Barcelona Wengerwas unwilling to take an unnecessary risk with his skipper.
Point of impact: Walcott (right) and Whitehead collide
The loss of Fabregas for the Wembley showpiece will come as a major blow to Wenger, who is already without Theo Walcott, Thomas Vermaelen and Lukasz Fabianski.
Walcott, who was also injured against Stoke after falling awkwardly following a challenge by Dean Whitehead, is facing a race against time to be fit for the game against Pep Guardiola's men in 12 days.
Wenger said: 'He has a classic ankle sprain. We don't think there is any more damage to it, but it is still a sprain. We are sad for him, too. He is out for Sunday and maybe one or two more weeks.'
Two down: Walcott (right) and Fabregas will miss the final
Robin van Persie, Laurent Koscielny and Alex Song will also have to prove their fitness for the final.
Arsenal goalkeeper Wojciech Szczesny's grandfather will leave Poland for the first time this weekend to watch the 20-year-old play at Wembley.
The youngster has established himself as the club's first-choice keeper and hopes to top off his rise to fame by lifting his first trophy.
'I have a few members of my family coming,' said Szczesny. 'My brother is coming and my grandad, Kazimierz, is leaving Poland for the first time in his life, so that will be a big occasion.
'He's in his 70s. I'm very pleased he's coming. He's watched me a few times for the national team. It's an extra incentive for me to do well.'
Final chance: Wojciech Szczesny (right) can't wait for his Wembley bow
Victory on Sunday would complete the first part of a possible quadruple for the Gunners, who can still win the Barclays Premier League, the FA Cup and the Champions League as well as the Carling Cup.
Szczesny insists, despite his meteoric rise, he is ready for his Wembley debut.
He said: 'It's down to the manager to make the decisions. Thankfully, I took my chances well and we have a chance to play at Wembley now.
'I didn't expect it to happen this quickly but I'm delighted with it. I'm very confident and I keep my feet on the ground. Nothing really fazes me. I was born this way.'
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Explore more:People: Cesc Fabregas, Theo Walcott, Arsene Wenger, Robin Van Persie, Laurent Koscielny, Dean Whitehead, Alex Song, Thomas Vermaelen Places: Birmingham, Barcelona, Spain, Poland