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, The Huddersfield Examiner reports.
Huddersfield sold one right-back, Tommy Smith, to Stoke in the summer transfer window, but brought in Herbert Bockhorn to compete with Florent Hadergjonaj in Simpson's position.
Nevertheless, the former Manchester United player's experience could come in use to a side which remains joint-bottom of the Championship.
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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