Since his death last week, calls from across the world have been made to find a suitable way to honour the popular broadcaster.
Suggestions have included renaming a stand at Murrayfield, erecting a statue outside the ground and a scholarship for training sports commentators.
Now the city's Lord Provost has welcomed the idea, saying the council is ready to lend its support to the most appropriate idea.
Cllr George Grubb said: "Bill McLaren was loved and revered by rugby fans the world over for his infectious passion for the game, his innate impartiality and his meticulous pre-match preparation. No doubt generations of players and fans would warmly welcome some form of public tribute to Bill's memory."
The commentator, known affectionately as "The Voice of Rugby", was laid to rest in his hometown of Hawick yesterday.
Scottish Rugby Union has confirmed it will sit down with his family to discuss possible options for celebrating his life and work.
And it has emerged that paperwork had been submitted in August in an attempt to have him knighted in the Queen's honours list.
Watsonians coach Bruce Aitchison, who started an online campaign to create Sir Bill McLaren, said: "I know it is very rare that anyone gets knighted posthumously, but with Princess Anne a major supporter of Scottish rugby and an admirer of Bill's, you never know.
"There have been a few options suggested, like naming a stand or creating a statue, but we have to make sure we don't rush into anything and what is done is right."
A Facebook group set up to name a stand at Murrayfield after the commentator has already attracted more than 5,000 fans, while discussions in Hawick are ongoing to have a statue erected.
Edinburgh West MP John Barrett said he has already held discussions with the SRU about ideas for a lasting tribute at Murrayfield.
"Bill was a nationally recognised figure and I think this would be a fitting tribute," he said. "It wouldn't cost anything because folk will want to make donations.
"The obvious thing is a statue, but there might be the possibility of a scholarship that would help people train to do the work he did – sports commentating.
"That's why it would be best to get all those interested to sit down and think it through.
"What I'm seeking to do is make sure a whole lot of people don't pull in different directions."
A spokesman for SRU said: "We are gathering comments and feedback from supporters around the world in respect to Bill McLaren's passing and will discuss it with his family.
"Anything that will be done in future will be with the full co-operation of his family."