Newcastle United came up against the France international at the start of the month.
It is claimed a transfer fee of £13.7 million would be considered realistic for Guilavogui, who played in the German side's 3-1 friendly defeat against the Magpies earlier this month.
Wolfsburg's Josuha Guilavogui in action against Real Madrid
However, Newcastle are said to face Champions League competition, with Nice boss Lucien Favre listed as another of the Frenchman's admirers.
And the Ligue 1 side are believed to have funds available, following the recent sales of Valentin Eysseric and Dalbert to Fiorentina and Inter Milan respectively.
A new defensive midfielder was not thought to be high on Newcastle's list of priorities heading into the final few weeks of the summer transfer window, with a new goalkeeper and striker being sought first.
Nevertheless, it is possible Guilavogui, who has been capped seven times by France, could come into the equation should those positions be filled - providing Toon boss Rafa Benitez is also able to offload those who are surplus to requirements.
Newcastle United boss Rafael Benitez (second left)