Cornes, 31, and Brogan 32, retired from the Power at the end of this season, with the former playing his farewell game in round 20 and the latter round 24.
Sheedy confirmed on Wednesday at the announcement of Callan Ward and Rhys Palmer as Giants the new club was keen on tapping into the combined 413 games of AFL experience the Port pair offered.
"We've had discussions with them, no doubt, and I've read that today," Sheedy said.
"If they're capable of wanting to come up here and help build this team, then we will be interested in those sorts of players and other players that would be interested.
"Remember, we were told 12 months ago that no one would want to come to west Sydney.
"The proof now is that a lot of people and players want to come to an area like Breakfast Point.
"We're really happy with the way this is rolling out."
Cornes played 239 games for the Power before failing out of favour with former teammate and Port coach Matthew Primus this season, while Brogan played 174 games but was limited by injury in 2011.
The Giants can take up to 10 players who have previously been on an AFL list as part of their list establishment rules.
Meanwhile, Giants' CEO Dale Holmes said he wasn't aware Melbourne young gun Tom Scully was poised to visit the club's facilities in the coming days, as reported by News Limited on Wednesday.
He also said there was no time frame on when Scully had to decide on whether he should accept the lucrative deal put forward.
"Tom and Melbourne are obviously going through their discussions. Where that ends, I don't know," he said.
"It's been well documented that we're interested in Tom, that's been on the table, it's up to Tom to decide what he wants to do.
"From our point of view, bringing in some experience and leadership into the club, some players with careers of 10-years plus who will actually come in and complement what we have with Callan and Rhys and some of the talent that's in the room, and what we get through the draft.
"Our list plan and our strategy for list development for the club is that we wanted to take a jigsaw approach where you put the pieces of the puzzle in first, which is the uncontracted players.
"You complement that with young talent, and ultimately you need some experience in the fist year or two as well.
"We're looking at bringing that all together."
Sheedy said he was yet to meet Scully, and even said he had not sat down with Ward or Palmer before Wednesday.
"[Scully] is a very good player and if he decides to come up here, we'll be rapt," he said.
"We've got four or five players who are training already this year who are very capable of playing League footy next year, and all of sudden, you're looking at about a dozen players for your midfield.
"If he's one of them, then so be it. I've never met Tom Scully and I hope I do meet him."
The Giants have also been reported to be interested in recruiting recently retired triple premiership Brisbane Lion Luke Power to their coaching stable.
The newest AFL club has the opportunity to lure uncontracted players to the club again in 2012, and also has up to four 17 year-old players they can offer for trade in the October exchange period.
