Graham represented the Gunners as a player and manager for a combined total of 15 years and 687 games.
He remains the second most successful Arsenal boss behind Arsene Wenger even if his reputation among some Gunners fans was sullied somewhat by his decision to manage bitter rivals Tottenham Hotspur.
But Graham was unperturbed by the result and told talkSPORT Arsenal will go on to win the Premier League.
"At the beginning of the season you always fancy Arsenal to finish in the top four," Graham told talkSPORT.
"But I think this season they're all ready and I think they will win it anyway.
"Leicester (have done well to be top) yes, but Arsenal definitely, I think Arsenal will win it this year."
'No need for new striker'
Graham also refuted suggestions the club needs to go out and spend big on a top striker in January to help seal a first Premier League crown for 12 years.
The 71-year-old said the Gunners have the money but believes they won't and don't need to bring anyone in.
He believes the rotation of Olivier Giroud and Theo Walcott depending on the opposition will be enough to secure title glory come what May.
"Everybody would like to go out and buy somebody from Barcelona," Graham added.
"I think Arsenal have got the money, but I don't think it will happen so they've just got to get on with it."