The one-time Premier League winner played an hour for the Owls Under-23s against Coventry City on Monday with first-team manager Darren Moore in the stands as he attempts to win a new contract for the first time since leaving Town at the end of last season.
The transfer window closed on February 1, but clubs are able to sign free agents to bolster their squad, just as the Terriers did with Yaya Sanogo.
The 34-year-old is perhaps a slightly more conservative full-back than Moore would ideally like as he tends to play with his high and wide, and even used wing-backs in Sunday's 2-1 defeat to Norwich City, but the experience he would bring to the club would more than compensate for it if he can prove his fitness.
Although he has been unattached this season, he has been playing for former club Leicester City's under-23s to use his experience.
Simpson was a fixture in the Foxes side that won the Premier League in 2015-16.
He has played Champions League football for first club Manchester United and Leicester, and Europa League for Newcastle United but also has recent experience of Championship relegation battles having been part of the Terriers side which stayed up last season. He has also played for Ipswich Town, Blackburn Rovers, Sunderland and Queen Park Rangers.
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