The Dubai club have run the UAE champions close in this season's Pro League and, with three rounds remaining, are favourites to secure second position in the standings.
However, Grafite has recently reiterated his desire to secure a trophy during his time at the Rashid Stadium, and last month signed a contract extension to keep him at the club until the end of the 2013/14 campaign.
Yet the Brazilian may not have to wait that long, as Ahli are two victories away from triumphing in the country's second-most significant competition. Should they defeat Al Ain on Sunday evening at the Al Nahyan Stadium they then face either Wahda or Al Shabab in the final on May 28.
Ahli last won the President's Cup in 2008.
Grafite is concentrating solely on Al Ain, the team he scored four goals against in Round 1, when Ahli enjoyed a resounding 6-3 win.
"Al Ain have proved they're a strong team after they recovered from their poor start to the season, but Ahli are also a strong competitor," said Grafite, who has 24 goals in 21 matches this season. "Everyone is focused strongly on coming out with a positive result that guarantees we qualify for the final and then have a chance to win the trophy that justifies the season."
Al Ain enter on the back of last week's disappointing exit from the Asian Champions League.
The Garden City club were beaten at home by the Iran aside Esteghlal, on Tuesday night, meaning they finished third in Group D.
They also lost the preceding Pro League assignment against Al Shaab, albeit with a weakened line-up.
While acknowledging Al Ain have not been as effective of late, Grafite has warned his teammates that is no cause for complacency.
"The task will not be easy," he said. "We cannot say Al Ain is weak due to the decline in results in the Champions League and the league recently, because it is not a measure of their ability.
"Cup matches are always unpredictable. It comes down to whoever puts in the largest effort and has the most presence throughout the 90 minutes."
Cosmin Olaroiu, the Al Ain coach, expects a difficult examination.
"We face a strong team who have the same ambitions of winning the competition, especially as they didn't succeed in lifting any title this season," he said.
"Both clubs know each other well having played only last month [in the league], and whoever keeps their cool and is highly concentrated will control the match."
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