The Kinks had hits with Waterloo Sunset and Lola
The Kinks singer Ray Davies has said the band are "three quarters of the way there" for a possible reunion.
"The stumbling block is my brother because he was seriously ill recently and whether he feels ready to do it," he told BBC Radio 4's Front Row.
Guitarist Dave Davies suffered a stroke after collapsing in June 2004.
The Kinks, one of the most popular rock bands of the 1960s, scored UK number one hits with You Really Got Me, Tired of Waiting and Sunny Afternoon.
The band went through a number of line-up changes over the years, and Ray and Dave had a volatile relationship. The Kinks last performed together in 1996.
"There is a desire to do it, but the thing that would make me decide yes or no would be whether or not we could do new songs, even if it's four or five," Davies said.
"But I couldn't do it just for nostalgic reasons."
"My pitch to the other guys in the band - because I'm really for it - was what would we have written if we hadn't have had our first hit, You Really Got Me?" he said.
"What if we put ourselves in that situation, what would have happened? So I think new work is important for artists as they mature and get older.
"The amazing thing is that The Kinks are the only band, of that period, where the only original members are still alive," he added.
Davies was speaking ahead of the opening of his new London musical Come Dancing, which he also stars in.
The musical, set in the 1950s around the Ilford Palais ballroom, includes over 20 songs by the singer.
The interview will be broadcast on BBC Radio 4's Front Row on Tuesday at 1915 BST.