The former Gunners manager feels the 21-year-old brings drive to the midfield and is backing the north Londoners to finish third in the Premier League.
Wilshere is currently sidelined through injury but could make a return to the team for the Gunners' game against Norwich on April 13 and Graham feels Arsenal needs him back in the side.
"Jack Wilshere is one of the few world-class players in the team," Graham said to talkSPORT. "He was out for so long and they missed him. He’s not only got wonderful technical ability, but he’s a natural winner. They need that drive from midfield, without question."
The Scot, who won two titles during his time with the north London club, also feels that the Gunners are now favored to finish in the top four, as he believes they have an easier road than Tottenham and Chelsea.
“I fancy Arsenal. I didn’t earlier in the season but now they’re favorites and could maybe even end up third," he added. “Tottenham have been outstanding this season. In the games I saw them play earlier this season I thought they would definitely be in the top four, but if you look at the fixture list they have got a very, very hard run-in.
"Arsenal’s only real tough game is away at Manchester United."
The Scot has also praised current manager Arsene Wenger, despite enduring another trophyless campaign, and says the team is picking up form at the right time.
“Arsene Wenger has been under a lot of pressure and criticism this season, some of it is justified, but when it comes to the run-in at the end of the season he’s been fantastic," he added. "They’re not the Arsenal of old but they’re picking up important points and playing with a lot of confidence."