The 20-year-old, who scored four goals in three Carling Cup matches this season, is rated highly by Arsene Wenger who may want the frenchman to get regular first-team football before the 2004/05 season starts.
Kinnear wants Premiership-standard players at the City Ground in his bid to avoid relegation and has the funds to do so following Michael Chopra's return to Newcastle after a month's loan.
Forest already have Nick Barmby, Alan Rogers, Andy Impey and Michael Stewart on loan deals but with Stewart and Barmby injured (both hamstring) and Rogers and Impey likely to return to Filbert Street, Joe could be short on numbers once again.
Players such as Matthew Upson and John Terry have had successful loan moves to the City Ground in the past to boost their careers - Aliadiere could well become the next.