Bergkamp injured his hamstring against Derby two weeks ago and was initially told he was likely to be out for at least three weeks - ruling him out of the final against Newcastle United when Arsenal can clinch the double.
But the Dutch forward has made considerable progress, yesterday passing the first test set by Arsenal's manager, Arsene Wenger, of kicking a ball without suffering a setback, and he is hoping to leave a decision on whether to play to the last possible minute.
He does not want to jeopardise his World Cup chances by coming back too soon but, having missed Arsenal's championship-clinching game against Everton, he is desperate to be involved at Wembley.
Bergkamp said: "At the moment my chances are 50-50, and that's more than I would have expected last week. There is still hope and it's getting better. But I still don't know if it's going to be enough for Saturday. I will have a fitness test tomorrow and if that's hopeful then we will wait until Friday."
He told ClubCall: "This is the kind of game you dream of, so I will do everything I can to play in it. I don't want to be stupid; I want to be sensible, but if I have a slight chance of making it I would do everything I can.
"Yet with a hamstring injury you have to be 100 per cent, because otherwise you can get yourself and the team into trouble. I want to be able to concentrate on my football rather than the injury."
Lee Dixon says he will definitely be fit to play on Saturday, despite missing Arsenal's last Premiership game of the season at Aston Villa last Sunday.
The full-back picked up a slight ankle knock last Wednesday against Liverpool but was fit to play against Villa and was rested as a precautionary measure.
Newcastle's Greek international defender, Nikos Dabizas, thinks the club's hunger for a winning climax to a traumatic season could give them the edge over double-chasing Arsenal.
Kenny Dalglish's players have suffered disappointment in the Champions' League and narrowly avoided relegation from the Premiership. Bad publicity from their FA Cup battles with non-League Stevenage and the lurid revelations of their former chairman and vice-chairman, Freddie Shepherd and Douglas Hall, have added to their woes.
Dabizas is confident that the Magpies can finish the campaign on a high note at Wembley. "Because this is all we can win this season and everyone makes Arsenal the favourites we have nothing to lose, so why shouldn't we fancy our chances? Maybe we are the ones starving for a win. I don't believe we are the outsiders, this is a different game to the league and anything can happen, especially with a great player like Shearer in the side.
"It is very exciting as the game comes closer and we believe we have the players to take the trophy back to Newcastle. But it would be dangerous for us to think of Arsenal just as individuals, like Bergkamp or [Patrick] Vieira. They're a team and if we beat them it will be because we've all played well.
"My dream has always been to score goals. A goal at Wembley is too much to hope for but you never know."
Dabizas, who only joined Newcastle from Olympiakos in March, is wanted to walk out beneath the Twin Towers.
"Before I came to Newcastle I always seemed to end up on the losing side in semi-finals but now I can begin to get excited at the dream of playing at Wembley in the FA Cup final.
"Throughout the world this is the match which everyone looks out for and now, after being at the club for less than two months, I'm hoping to be part of it."