Tottenham held a seven-point advantage over Arsenal, but a recent poor run of form for Spurs - which continued on Sunday with a 2-2 draw against Everton - means the Gunners are now favourites for Champions League qualification.
Should Arsenal win their home clash against Norwich on Saturday they will move ahead of Andre Villas-Boas' men with just six games of the season remaining.
And with Spurs yet to play Chelsea and Manchester City, Graham, who managed both clubs either side of the north London divide, reckons Arsenal will beat their rivals to fourth place.
"I fancy Arsenal [to finish in the top four]," Graham told talkSPORT.
"I didn't earlier in the season but now they're favourites and could maybe even end up third.
"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.
"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.
"They're not the Arsenal of old but they're picking up important points and playing with a lot of confidence."
Arsenal's hopes of overcoming the Canaries this weekend have been boosted by the news that Theo Walcott and Jack Wilshere are due to return from their respective hip and ankle injuries.
Wilshere was in superb form until he suffered the injury in March and Graham thinks the Gunners will only get stronger when the England star returns.
"Jack Wilshere is one of the few world-class players in the team," Graham added. "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."