The Malaysian businessman was behind the controversial decision to dispense with tradition and change the Bluebirds' home kit to red, but appears now to be prepared to at least think about reverting back.
Cardiff were relegated last weekend after a turbulent first season in the Premier League, with manager Malky Mackay dismissed in December and his successor Ole Gunnar Solskjaer unable to keep them up.
Tan has now said that should the club bounce back to the top flight, he might be prepared to concede on the club's colours, having believed a change to red would make the club more marketable overseas, especially in Asia.
"I would like to focus on getting back to the Premier League and after we are there I will definitely agree to sit down and find a solution - maybe we can have a compromise," he told the BBC.
"I am not a quitter. I will stay until we get ourselves up and then we will see whether we can work out this colour change and compromise. If we can, maybe I will stay for a long time."
He added: "Let us get back to the Premier League first and after we are there I assure fans, the Supporters' Trust and all of them, that I will sit down with them and we will find a solution that I hope will be satisfactory for all - for them and for me also.
"We would like to work closely with the fans. We will try to engage and meet as often as we can.
"Our chairman (Mehmet Dalman) will have constant dialogue and whenever I can I will join them."
Tan has also rejected his image as a 'villain' after reaching a settlement over the sacking of Mackay.
The Scot and his former head of recruitment Iain Moody both released statements on Friday announcing that they had reached settlements with Cardiff and also issued apologies for any offence they may have caused to Tan.
"For legal reasons I cannot comment on the detail," Tan said.
"But I'm pleased that finally we have a closure on this matter and suffice to say he is dropping all litigation, all claims against us.
"I'm pleased with the result and I'm also pleased that he has publicly apologised. I said before, one day some people will apologise to me for what they have done.
"Some people made me out like the villain. I'm supposed to be the Bond villain, but actually I'm James Bond."
- Sports & Recreation
- Premier League
- Malky Mackay
- Ole Gunnar Solskjaer