The 18-year-old initially joined the National League club on a month-long deal, and has started four games in all competitions for The Spitfires.
Odoffin is working under Eastleigh manager Martin Allen, who gave him his Barnet debut before the defender moved to Molineux in January 2016.
He is yet to make a senior appearance for the Championship club.
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Eastleigh have extended the loan of Wolverhampton Wanderers defender Hakeem Odoffin until the end of the season.