"All the ex-players want Leeds United to do well. We are still very passionate," Billy says. "I'd love to see the club on the European victory trail again. We won the old Fairs Cup twice during my time and I think the present side could go a long way in the UEFA Cup."
But the Elland Road old boy has a word of caution.
"In my view, it's probably the hardest of all the European competitions to win, partly because there are so many rounds."
Ironically, Bremner originally never really wanted to come to Elland Road. He'd made a big impact with Scotland schoolboys in the mid-to-late 1950s and a host of top English clubs were soon chasing his signature.
"There was me and a boy called Tommy Henderson," he recalls. "We played against England schoolboys at Wembley - a side which included the likes of Terry Venables. Everyone was showing an interest in us. We spent a couple of weeks training with Chelsea and 10 days at Arsenal, but I had always wanted to play for Glasgow Celtic. My father was dead against that because of all the religious conflict in Glasgow."
Bremner wasn't too enthusiastic about the prospect of moving to Leeds United, a club that he knew nothing about, although he had heard of the great John Charles. But he was eventually persuaded to sign for Leeds in 1958.
For a man whose name became synonymous with Leeds Unrted, Billy Bremner wasn't keen to stay at Elland Road when he first arrived. He was always looking for possible escape routes back to his native Scotland.
"I kept setting myself what I believed were impossible targets and saying that if I didn't achieve those targets then I would go home."
But the former Leeds skipper's plans backfired because, as the targets were set higher, the more easily he achieved them.
"I never thought I would make the reserves by the age ot 16 but I did. I never believed I'd be in the first team at 17, but sure enough I managed it. It came to a point where I simply couldn't go home."
In 1961 Bremner linked up with the man who was to lead the Elland Road club to the most successful period in its illustrious history. To this day Billy still refers to Don Revie as "the Gaffer".
"I always say my father was the biggest influence on my football career," says Billy, "but Don Revie came a very close second. He made a tremendous impact on Leeds United. He was a new, modern breed of manager, who was always accessible to the players. In the old days, football managers could be remote figures. But not the Gaffer."
Revie struck up a remarkable bond with his players and when they went out on the pitch they were prepared to die for him. Bremner was a pivotal figure in the Leeds side which became one of the most feared and respected in Europe. Bremner went on to win two League Championships, the FA Cup, the League Cup and the Inter City Fairs Cup twice in a remarkable 17-year career at Elland Road. He also won 54 Scottish caps and the Footballer of the Year award in 1970.
The former Leeds captain is still a regular match goer in his capacity as a television and radio summariser. He also goes to matches socially with former Leeds favourites Allan Clarke and Mick Jones.
"All the ex-players still keep in touch," he confirms. "We still have a tremendous rapport. We used to live in each other's pockets as professional players and we still retain a very special bond. They're a great bunch of guys. I think the Gaffer's responsible for that. He had 16 internationals in the first-team squad and yet there were no stars. We were all treated the same and that created a tremendous family atmosphere. Don Revie wouldn't have had it any other way."
Bremner had a three-year spell in charge at Elland Road after turning to management when his playing career ended, but he was never able to recreate the success he enjoyed as a player.
"I'd still like to get back into football management if the right offer came along. But I miss the playing side most. It's not so much the admiration and the big crowds, it's more the comradeship and the banter in the dressing room."
Billy, like all the players of his day, has seen the game change dramatically since the 1970s.
"It's big business nowadays," he sighs, "but there are still a lot of players around to admire. Alan Shearer would be considered as outstanding in any era. I reckon he's one of the top players in the world at the moment and such a tireless worker for his team-mates."
The former Leeds captain is also a big fan of the current skipper at Elland Road.
"Gary McAllister is a hugely talented player in midfield. I hope he can lead them to the UEFA Cup Final."
Bremner remains a football man through and through and will go down as one of Leeds United's greatest stars - a man who came to love a club he'd never originally heard of.
Born: December 9,1942
Leeds League & Cup apps: 770 (plus 1 sub)
Leeds goals:115
Other clubs: Hull City, Doncaster Rovers
International: Scotland, 54 caps
Honours: League Championship (1968-9,1973-4), Second Division
Championship (1963-4), FA Cup (1972), League Cup (1967-8),
European Fairs Cup (1967-8,1970-1)