Steve Bruce is keen to bolster his defence with the arrival of one more centre-back as his side are set for a testing campaign with domestic and European commitments this season.
The Tigers have already added Harry Maguire to strengthen the backline and Bruce has been chasing Michael Dawson for much of the summer.
The Spurs defender looks unlikely to make the move to Hull now because the two clubs have been unable to reach an agreement over the transfer fee, and a move for German defender Wollscheid is now being weighed up.
A host of Premier League clubs are also interested in the Leverkusen man with Southampton, Sunderland and Newcastle also linked with a move.
The 25-year-old made 20 appearances for the Bundesliga side last season, but Hull will not be getting as good a defender as Dawson if they pursue Wollscheid.
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Dawson outperformed Wollscheid in several key defensive areas last season and the Tigers should perhaps return to Spurs with an improved offer rather than chasing Wollscheid.
The German did see much less action than the Spurs man, but his lack of Premier League experience will make signing him a gamble.
Hull have plenty of options at the back, but with Bruce likely to stick with three central defenders, he will need lots of options in what will be a testing season for the Tigers.
They got the season off to a fine start with a 1-0 win at Queens Park Rangers on Saturday, and they travel to KSC Loveren in the Europa League on Thursday before hosting Stoke next Sunday.
Would Wollscheid be a good signing for Hull City?