The full back fell out of favour after Jose Mourinho took the Spurs hot seat, only featuring three times in the Premier League after the former Manchester United manager was appointed in November.
Speaking to the Second Captains podcast, Rose said: "I am very happy to stay at Tottenham and see my last ten or 11 months out, I would love to. There is nothing I want more than to play one more time in front of the fans.
"My last game for Spurs was a 1-0 defeat to Liverpool and at the time I didn't know that was going to be or could be my last game for Spurs."
Having spent 13 years with Tottenham, the club and fans hold a special place in Rose's heart. The England international cited his love for the supporters as a huge factor in his desire to play for Spurs again.
"I want nothing more than to play in front of the Tottenham fans one more time, just to cherish all the moments we have had over the years with them.
"They have always been good to me, I have possibly given them reasons in the past not to be so good to me, but they know when it was game time I gave everything for them.
"I would love nothing more than to play one last time for Tottenham and just be able to say goodbye to them and thank them for everything they have done for me as a person as a player. Ultimately, as good as I am or was is because of the love they gave me."