The Republic of Ireland international is understood to have agreed a half-season loan at Elland Road and was due to complete his transfer ahead of the start of the new Championship campaign on Saturday.
O’Dea will provide United with an extra centre-back and another means of addressing the poor defensive record which hampered the Whites in the Championship last term.
The 24-year-old holds prior experience of England’s second tier having completing loan spells with Ipswich Town and Reading in the past two years.
O’Dea played eight times for Reading in 2009 and made 25 appearances for Ipswich last season, including one against Leeds in a goalless draw at Elland Road in March.
His outings with Celtic number more than 50 but the Scottish Premier League club have a surplus of defenders in their squad, and O’Dea has not featured in the opening stages of their domestic term.
Grayson is already in possession of a wide selection of central defenders and the re-signing of Patrick Kisnorbo on a two-year deal last month increased his pool to five.