Celtic claim a fee was agreed with Manchester City for John Guidetti prior to them taking the striker on loan.
Xabi Alonso claims no Premier League offers were put to him before leaving Real Madrid for Bayern Munich.
The Texan businessman has drawn up a list of potential replacements for the 45-year-old Italian with former Brighton manager Gus Poyet having emerged as the leading candidate.
However, Short, having been forced to relieve Di Canio of his duties after just 175 days and only 13 games, is determined to get it right this time around.
As a result, he will iron out any potential problems before he makes an appointment, and have a series of contingencies in place.
Reports from Italy have suggested Poyet has all but got the job, but Press Association Sport understands that while the Uruguayan is currently the preferred option - Sky Bet were quoting him as a 1/8 favourite on Wednesday - no concrete decision has yet been taken.
As a result, development coach Kevin Ball, who threw his own hat into the ring after Tuesday night's 2-0 Capital One Cup third round victory over Peterborough, will continue at the helm as the Black Cats prepare for Sunday's Barclays Premier League visit of Liverpool to the Stadium of Light.
Asked how long he expected to remain in his interim role after the game, Ball said: "At this moment in time, until Sunday.
"They asked me to take tonight and Sunday. If anything changes between now and Sunday for whatever reason, so be it, but at the moment, I believe it is until Sunday, and then obviously we will take things from there.
"I would like to think we will talk sometime tomorrow to have a chat about how things are going.
"I know it sounds a cliche, but you talk about one game at a time and I don't think I can do anything more than that. We will just wait and see what happens."
However long his time in the limelight lasts, Ball will at least be able to reflect upon a successful start.
Having been asked to wade into the mess left behind by Di Canio, the former Black Cats midfielder managed to mobilise a dressing room left shell-shocked by the excesses of the Italian's brief reign to produce the most convincing performance of the season to date, albeit against opposition they were expected to beat comfortably.
Ball handed former captain Lee Cattermole, who had been discarded by the former Swindon boss in pre-season, a central role and asked summer signing Emanuele Giaccherini to play in the hole behind lone striker Jozy Altidore.
The pair combined to good effect with 32 minutes gone to give their side the lead, the Italy international firing home from the midfielder's cross, and victory was secured 17 minutes from time when substitute Valentin Roberge headed home a second goal.
Ball was particularly pleased with Cattermole's contribution after working with the 25-year-old in pre-season following his exile to train with the under-21s.
He said: "What I enjoyed most about him was seeing his professionalism and how he went about things, how he did things and how he demanded from the under-21s.
"Sometimes, I have to say, it put a little smile on my face because it reminded me of when I played.
"You could see some of the under-21s probably thinking, 'He's having a go'. But I said, 'Listen boys, that's what you have got to accept. He's not having a go at you to have a go at you, he's pushing, he's demanding from you'.
"When you saw Lee on the pitch, bearing in mind he hasn't played 90 minutes for a long period of time, he put in a very accomplished performance, along with a fabulous ball for the goal, and he drove people on.
"But that was one of many good performances."
Indeed, it was the collective effort rather than those of individuals which pleased Ball after a traumatic 48 hours on Wearside.
He said: "All I can talk about is since I stepped into the breech, so to speak. They displayed a lot of confidence yesterday in training, they worked very hard, they were very professional and you have to give them credit."