Simpson, 34, played an hour of yesterday’s under-23 clash with Coventry City and is available on a free transfer having left the Owls’ next opponents, Huddersfield Town, last year.
A Manchester United academy graduate, he went on to play at Newcastle United and QPR before a five-year Leicester spell in which he won English football’s ultimate prize in 2016.
At Huddersfield last season he made 24 league appearances and left in headline-claiming circumstances amid confusion over the extension of his contract in June last year. He’s since been training and playing with Leicester’s under-23 side last month.
So given his time out of the game at first team level, would Simpson really be capable of making an instant impact on Wednesday’s struggling survival bid?
We spoke to former Terriers stopper Matt Glennon, Radio Leeds’ Huddersfield Town co-commentator, for the inside track on Simpson and what he would offer the Owls.
How was he at Huddersfield and what do you make of the Owls link?
Huddersfield needed someone like that at the time, that experienced head who has been there and done that. They were on a complete downward slide but he came in and had a really positive impact on the squad, you could tell straight away he was a winner, he wanted to do well.
He's not someone who walks around the pitch showing off his medals put it that way, he was up and down, throwing himself into challenges and he had quality. And the bottom line is he wants to be part of teams that are winning football matches.
It's not an easy move if he takes it, Sheffield Wednesday but he could be the character they need in there right now, a bit more experience to come in and help out.
What sort of role did he play?
He was playing a right-back, but he got forward a lot. And he started really, really well.
Straight away he made that impact and looked a real quality player, which was impressive given he'd not played loads of games and was coming in cold.
But then he had a couple of injuries, a couple of things happened and it started just to drop a little bit form-wise as it did with the team as well, but then he collected himself and came on strong again.
Would you expect him to be able to hit the ground running with Wednesday?
He'll have been looking after himself, for sure, he's that type. The fact that he’s been in training at Leicester will be a good sign as well. They're not just going to let him come in and do nothing.
When they have someone in like that they have to set an impression for the younger players, Brendan Rodgers won't have had him coming in and going through the motions.
He's a Premier League winner with Leicester at the end of the day and he'll have been working hard.