The England Under-21 international signed for the Championship club earlier this week after failing to cement a first-team spot at the KC Stadium.
The initial loan deal runs until December 28, but Ince would be happy to remain at the City Ground if both parties agree.
"The Premier League is where I want to be but I'm still 22 years of age," Ince told Forest's official website. "I have a lot to learn so to have the opportunity the gaffer has given me is fantastic.
"If, after the two months, I've had a great loan spell and both parties are enjoying it then there's definitely not a dead end."
Ince turned down Inter Milan before joining Hull in the summer.