The 18-year-old joins the Dens Park outfit until the end of the season.
Dark Blues boss Barry Smith is also keen to recruit a striker in a bid to boost the club's survival hopes.
Dundee currently sit 14 points adrift at the bottom of the Clydesdale Bank Premier League.
A statement on the club's website confirmed: "Dundee football club are very pleased to announce the signing of David Morgan on loan from Nottingham Forest until the end of the season.
"The-18-year old midfielder has already represented Northern Ireland at Under-21 level.
"The club can confirm they are still in pursuit of at least one striker that will not necessarily be affected by the transfer window."