The debt to Swiss-based financial company Langston, of whom former Bluebirds chief Sam Hammam is a representative, was taken out in 2004 and is believed to be worth £24million.
Cardiff's most recent financial figures showed the club are £83million in debt.
Tan revealed he has held talks with Hammam, who he invited to Cardiff's home game with Bolton in April to witness the club receiving the Championship trophy, and is hopeful a deal can be struck soon.
Should negotiations conclude successfully the Malaysian said he would convert the substantial amount he is owed by the club into equity.
"We are talking to Sam Hammam to try to resolve the Langston issue," Tan told a press conference at the University of South Wales in Treforest, where he received an honorary doctorate.
"I have been talking to Sam. We have been friendly, talking. I like to regard Sam now as my friend and we will come around and resolve this. We are, I think, days away from an agreement."
Tan added: "We are days away from an agreement and then we can convert all the loans to equity. That will make us much more secure and hopefully debt free, which is good. That's my goal - to make the club debt-free, so that the club won't be under any threat and after that we just have to manage it prudently, run it like a business."
Tan, however, was also critical of a section of the club's support. Some fans remain unhappy at the move to change the colour of the club's home shirts from blue to red. The Malaysian has called on all supporters to get behind the club, but suggested he would be willing to walk away if enough fans opposed his running of the club.
He said: "I want to be here for as long as I am very welcome. If too many fans show we are not welcome, maybe you will have a new owner. But right now my experience is we are very welcome. We need the fans to support us and not be negative or disruptive or unnecessarily criticise us too much."