Dens Park manager James McPake is keen to reinforce his defensive options, and has also run the rule over former Dundee United centre-back Paul Watson.
However, The Sun reports that Urhoghide could be an option for McPake and that Dundee and Celtic have discussed the possibility of a loan move until the end of the season.
Dundee already have Leigh Griffiths on loan from Celtic, although there is the potential for that deal to be terminated this month.
Urhoghide signed for Celtic from Sheffield Wednesday during the summer, but has struggled to break into the first team under manager Ange Postecoglou.
The Glasgow outfit are keen for the 21-year-old from the Netherlands to get more minutes under his belt and are open to a loan move in this window.
Clubs in England are also keen to land Urhoghide, with proposals coming in from Championship and League One.