The former Cork City forward was poised to sign for Fulham last summer when Keane stepped in at the 11th hour to lure him to Wearside.
And he is confident the reputations of the club's manager and chairman will count for a lot in this summer's transfer rush.
O'Donovan said: "I knew it was a big club before I came in but it has surprised me just how big it is.
"The Irish connection, with the manager, the chairman and all the money that has come in, can be a big factor in our future success.
"It's been well documented what a good job they have done and it can help attract players to have those big names like Niall Quinn and Roy Keane in charge of the club.
"That is why I signed. In Ireland right now Sunderland are as big as Arsenal and Manchester United and it's great to have that behind you."
Keane has promised changes to his squad again this summer, but O'Donovan hopes to avoid the cull.
He made four starts and 13 substitute appearances in the Premier League during his debut campaign on Wearside and said: "The gaffer hasn't said anything negative to me, but everyone is on their toes.
"It doesn't matter how long our contracts are here, anyone can go.
"He enjoys players having to be on their guard all the time. He'll leave players out and you can see that when they're not in the team they're champing at the bit to get back in. There is a real hunger among all our players.
"It worked during the season."
H Sunderland striker Andy Cole, who is out of contract this summer and will not be offered a new deal, has rejected a permanent move to Burnley.
He ended the season on loan at Turf Moor and was asked to stay, but Clarets boss Owen Coyle said: "''We loved working with him and I think he loved it at the football club, but he had a decision to make and he's made it, which he is within his rights to do.
''The bottom line is the deal's not suitable to him."