The TalkTV presenter broke the news that Rubiales was resigning from his role with the Spanish FA following his poor conduct at the Women's World Cup.
The 46-year-old came in for intense criticism for kissing Spain player Jenni Hermoso on the lips following the nation's victory over England in Australia last month.
Hermoso, one of Spain's leading players, said that the kiss during the World Cup presentation ceremony was not consensual and has since filed a legal complaint against Rubiales.
In a small extract of the interview on Piers Morgan: Uncensored, Rubiales said: "I love my daughters so much and they love me so, so much. I am very happy and very proud of them. They are very near to me.
"About my resignation, yes, I am going to do [it]…"
MORE ON LUIS RUBIALES
Rubiales resigns as Spanish Football Federation president in interview with Morgan
Jorge Vilda sacked as Spain's women's coach just two weeks after winning World Cup
Morgan responded: "You're going to resign?"
Rubiales replied: "Yes, because I cannot continue in my work."
Morgan's interview was quite a scoop and appearing The Sports Breakfast with Andy Townsend and Ally McCoist, the TalkTV presenter said: "It was a bit cloak and dagger for the last two days.
"Through one of our brilliant bookers, we managed to track down a number for him and we had a series of conversations, I spoke with him at length a series of times and he couldn't really work out what he was going to do - whether he was going to stay or if he was going to resign, whether he wanted an interview or not.
Most read in Football
Ronaldo escapes red card for tackle that had Dubravka praying studs didn't catch his face
Rubiales resigns as Spanish Football Federation president in interview with Morgan
Lewandowski's manager denies claims he made Polish FA pay trip to Salt Bae's restaurant
Shaqiri places his hand on his heart during Kosovo national anthem as Switzerland player
"This went on for the last week or so and then he decided that he wanted to do it.
"He got on a plane; he flew to London and we actually did it in the News UK building in one of the empty floors and it was an extraordinary interview.
"It took two hours because it was party in Spanish and translated and partly in English so that we could break it to both, he was keen not to be misquoted because of the legal actions that are going on and at the centre of it, he absolutely accepts that he should never have done what he did.
"His behaviour was unacceptable, inappropriate and it took all of the spotlight away from what was an incredible win for the Spanish Women's team, but he doesn't dispute any of that.
"The point of dispute is that he is adamant that what happened was consensual and he's now facing a potential criminal prosecution - Jenni Hermoso has now advanced that so that he can now potentially be prosecuted and it just raises the debate about whether what we all witnessed on that podium could possibly constitute a crime or if it was just a guy who got completely carried away and stole the women's thunder and should rightly be castigated for that after losing his job for it along with the coach, of course, who led them to this glory.
"It's a bizarre situation where you've got a team who win a World Cup and you've got a coach who took them there and the president of the football association losing their jobs.
"It's a strange set of circumstances and I've spoken to a lot of people about it, but opinion is quite split over it."
Asked if Rubiales has issued a public apology to Hermoso, Morgan added: "I pushed him a lot on whether he wanted to personally apologise to Jenni Hermoso.
"I won't ruin what his answer is because it's a fascinating exchange that went on for quite a while where we went over this point.
"Having lost his job he's now facing the prospect of a criminal trial and if he's convicted, then going to prison and that's now what he's most concerned about.
"I pushed him hard on all the stuff you'd expect me to.
"He's very reflective about what has happened and searingly honest in parts about stuff, but also pretty determined that his narrative that he did nothing that was non-consensual, he doesn't deviate from that. Obviously there's a clear difference of opinion on that.
"I played him a series of videos, one of all the Spanish Women's players on the podium, and he does hug and kiss all of them. It's just that Jenni Hermoso he goes one step further and kisses her on the lips, so he's pretty tactile with all of them.
"I also played him the video on the team bus and the dressing room where Hermoso and the other women appear to be having a bit of fun about it all, showing each other pictures of the kiss and chanting 'presi, presi' about him and chanting 'beso beso', which means 'kiss, kiss'.
"It's complex. I don't think that this is a particularly simple thing because you've got a group of women who clearly find it all quite funny in the immediate aftermath, but perhaps in the cold light of the next day, maybe they start to think that this is all completely out of order, which is what a lot of women think."
Read More on talkSPORT
Djokovic hugs McConaughey and pays tribute to Bryant as he makes history at US Open
Rubiales resigns as Spanish Football Federation president in interview with Morgan
For the full interview, with more stunning revelations tune in to Piers Morgan Uncensored on Tuesday at 8pm. Watch Piers Morgan Uncensored, Monday to Thursday on TalkTV at 8pm.
Available on Sky 522, Sky Glass 508, Virgin Media 606, Freeview 237 and Freesat 217 as well as on DAB, Amazon Fire TV, Apple TV, Samsung TV Plus, YouTube, the Talk.TV website and TalkTV iOS and Android apps.