Bayern Munich forward Toni Kroos left the door open for a switch to the Barclays Premier League in the summer.
Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
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.