Ngoo is a free agent after leaving Liverpool earlier this summer upon the expiration of his contract at Anfield.
Liverpool beat a host of clubs to Ngoo's signature when they signed him as a 16-year-old for £250,000 from Southend in 2009.
The giant striker, who has represented England at Under 19 and Under 20 level, never made a first-team appearance during his time at Liverpool.
Ngoo enjoyed a successful spell on loan at Scottish side Hearts in the 2013/14 season, scoring five goals in 17 appearances before further loan spells at Yeovil and Walsall.
Odense are now hoping to lure Ngoo to Denmark as they look to beat a number of English clubs to his signature.