The group's frontman and chief songwriter Ray Davies said the reunion was as "close as it's ever been to happening".
The 69-year-old, his guitarist younger brother Dave and original drummer Mick Avory - the three surviving original members - all told Uncut magazine they are keen to get back together for the 50th anniversary of their debut release this year.
The siblings have had a famously fractious relationship, even in the early days of the group whose hits inluded Waterloo Sunset and You Really Got Me.
But Dave, 66, said he and his estranged brother had met up in a pub in Highgate, north London, last summer to discuss how they would mark the occasion.
He said: "We got together in August and the first few days were beautiful. We went up the pub and had a few Guinnesses, and we were talking about all kinds of s***, the old days and what-ifs.
"I said to Ray I thought that it'd be a great shame if we don't try and do something. I don't think our love has diminished. I think the stage-play has played itself out a bit, the pretence and the acting. I think it's time reality took over, and started directing the last years of... whatever it is. It's like Cain and Abel."
Avory, who left the band in 1984, said: "I think it would be nice to do something all together. Because the chances are diminishing as we talk.
"Hopefully me, Dave and Ray can meet before it happens. We'd have to knock our heads together and rehearse, if we meant to do it properly. We haven't played together for God knows how long."
But Dave admitted having some reservations, saying: "I don't want to see the legacy of The Kinks soured by two miserable old men doing it for the money."
The group's last album was in 1993 and their final public performance took place in 1996. Original bass player Pete Quaife died in 2010.
Ray headlined a free concert in Hyde Park in July last year after Sir Elton John cancelled his headlining appearance at Barclaycard presents British Summer Time due to illness.