Rose is a free agent after ending a 14-year stay at Spurs at the end of his contract last month.
The left-back was frozen out of the first-team squad for the whole of last season and last made an appearance for Spurs in a defeat to Liverpool in January 2020, before a loan spell at Newcastle.
The 30-year-old revealed he had used his time in the wilderness to connect with the club's younger players and said chairman Daniel Levy, with whom his relationship has often been difficult, has offered him the chance to return to Spurs in the future.
"I was given an opportunity this season to pass some of that knowledge on to the younger lads," Rose said in a farewell interview with Tottenham's in-house media team, released on Friday.
"They've become a part of me and I see them all as my little brothers.
"I've seen how hard they work, the looks on their faces when they say, 'I'm with the first team today'. It's been priceless. I've witnessed first hand what it means to them.
"I just had a meeting with the chairman this morning. He was asking me if I need any help with anything, said I'm welcome to come back in the future.
"I'm over the moon I did make that choice to come here in 2007 and I look forward to coming back after I've finished playing football and hopefully having an impact on the younger age group again, like I've had this season."
Under Levy's chairmanship, a number of celebrated former players have returned to the club as coaches, including Ledley King and Ryan Mason, who was interim head coach for the final seven matches of last season following Jose Mourinho's sacking.
Rose joined Spurs from Leeds United as a teenager in 2007 and made 214 appearances for the club, playing a key role in their run to the Champions League Final in 2019.
He strained relationships with an explosive interview on the eve of the 2017-18 season, in which he took aim at the club's transfer policy, wage structure and ambition, telling Spurs to sign big names, "not players you have to Google and say, ‘Who’s that?’"
His relationship with supporters was also mixed after he was left dismayed by the reaction on social media to his new long-term contract at the start of the 2014-15 season.
But Rose thanked Spurs fans, said he would miss them and reiterated his desire to return to the club.
"I leave the football club a better person, a better professional, a better human being than when I arrived 14 years ago," he said.
"I get stopped in the street and they thank me for everything. I just want to say thank you for the love and support you've given me over the 14 years.
"I'm going to miss all the fans, miss everybody who's been involved in Spurs and I look forward to coming back one day. They'll be part of my heart for a long time and I'm going to miss them.
"There's been some amazing games I've been a part of. We played a great game against Chelsea we won 5-3 at the Lane.
"We drew with Arsenal 2-2 at the Lane, just in terms of atmosphere that was brilliant and Harry [Kane] scored an outrageous goal when he was wearing the eye mask.
"There's been a lot. When I look back there's quite a few games I feel lucky to have been a part of.
"I'm grateful for the club for bringing me in in 2007 as a 16-year-old and I feel very privileged to have experienced some of Tottenham's great days over 14 years."