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.
It would take a sizable investment to prise the England Under-21 international away from White Hart Lane - a figure of around £8million has been mentioned - but such has been the player's impact that there is an appetite to secure his services on a permanent basis.
However, despite former manager Martin O'Neill having broached the subject before his departure, there has as yet been no conversation on the topic with successor Paolo Di Canio, and Rose is comfortable with that.
He told the Journal: "I have thought about my future. When Martin O'Neill was here we did speak briefly.
"That has changed and it's not the time for me to go speaking to the new manager about what he wants for next season.
"The main priority is to have Premier League status for next year. Once that's sorted, once we are safe, I'm sure there will be a conversation to be had.
"I know what I want to do next year and we will just see what happens."
Whatever happens during the weeks and months ahead, Rose will look back on his year at the Stadium of Light with great affection.
Asked if he had benefitted from the experience, he said: "One million per cent, yes.
"I met Martin O'Neill before I signed and he said I would play more games here than I would do at Tottenham this season.
"He was 100 per cent right. I don't know what next season holds for me or what the next 10 years hold for me. Whatever happens, I will be forever grateful to Martin O'Neill for bringing me here."