Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
Hulse is well down the pecking order at Loftus Road and has not featured for them this season after being left out of their 25-man Premier League squad.
Hulse scored three goals in 15 appearances for Charlton in a three-month loan spell at Charlton earlier this season.
Millwall have been in the market for forwards after seeing Darius Henderson leave for Nottingham Forest and Chris Wood head to Leicester.