The 25-year-old centre-back spent the first half of the season on loan at Mainz but, after making only five Bundesliga appearances for the club, he looks set to arrive in the Premier League for the remainder of the campaign.
Captain Ryan Shawcross has been a mainstay at the heart of Stoke's defence this season, but Wollscheid would give Hughes another option in addition to Marc Muniesa, Marc Wilson, Robert Huth and the versatile Geoff Cameron.
The Stoke boss has been impressed with what he has seen of the Germany international, and expects him to provide good competition for places.
"It is a deal that is likely to happen and we are likely to see him [Wollscheid] here early next week I would suggest," said Hughes after Stoke's 3-1 win over Wrexham in the FA Cup third round.
"He has superb quality and in my opinion he is a very good footballer, so we are very pleased to have agreed the terms of the deal.
"He has moved for decent money in the past and he has played for the reigning world champions, so he has real good pedigree."
Wollscheid's arrival could spell the end of Huth's time at the Britannia Stadium.
The former Chelsea and Middlesbrough defender is fit again after a lengthy spell on the sidelines and featured against Wrexham on Sunday, but has been unable to break into Hughes' line-up for Premier League matches.
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