The Sun claimed earlier this month that Simpson was spending time with West Brom's Under-23s as the Baggies considered offering him a contract, which he could sign at any point after Leicester released him in June.
But that now seems unlikely after the 32-year-old took part in Terriers sessions on Tuesday and Wednesday, according to The Huddersfield Examiner.
Huddersfield sold one right-back, Tommy Smith, to Stoke in the summer transfer window, but brought in Herbert Bockhorn to compete with Florent Hadergjonaj.
However, some of a Terriers persuasion would welcome another addition in the pair's position - including Simpson himself.
Get Danny Simpson in with his mate Fraizer— Mac Bramadl (@Bramald) September 18, 2019
Danny Simpson can't be worse than Flo, surely? Even injured I bet hes just as good— Angry Berry (@Berrrrrrrrry) September 18, 2019
If Danny Simpson is even slightly interested in signing he should already be signed. We are dog shit on both sides at the back— Luke Nicholson (@luke_htfc) September 18, 2019
Danny Simpson ticks all the right boxes for me, experienced, not scarred with being part of that awful relegated team and been promoted from this league few times #htafc— bigelbow (@AlanAlanLee19) September 18, 2019
Buzzing with Danny Simpson. Done it all before and a leader.— Danny (@Danny__Ward) September 18, 2019
I’d take Danny Simpson in a heartbeat. A lot more reliable than Flo— Terry ⚽️ (@bluearmyhtfc) September 18, 2019
Danny Simpson or Flo? DS everyday of the week. Get him in for the rest of the season.— Terry ⚽️ (@bluearmyhtfc) September 19, 2019
danny simpson would be great for us, flo has made so many mistakes this season unfortunatly so hats off to phil for getting this sorted out before january. #htafc— Return of the Town (@ReturnTown) September 19, 2019
Not sure what you are thinking , but if you don't see Danny Simpson an an improvement on Flo. You don't know much.— BOB GRAHAM (@ROBERTGRAHAM320) September 19, 2019
Solid right back. I’d be delighted ⚽️⚽️⚽️— Chris Kerry (@CKterrier87) September 19, 2019
Danny Simpson - with dressing room with flat broken players. Signing big wage ego player isn’t really going to give us much. Prefer a youngster tbh #htafc
And the following Leicester fan appears to concur with most of his Huddersfield counterparts...
Won’t get a better right back was one of most underrated players during our title winning season wish we never let him go tbh— Liam Brown (@Liam90Brown) September 19, 2019
There is little to suggest at this stage, however, that Huddersfield are considering offering a contract to Simpson.
But if a move were to happen this week, then his debut could arrive against West Brom at The Hawthorns this weekend.
Would the former Leicester defender and recent West Brom trialist be a good addition for Huddersfield?
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