Club chairman Alex Harkess, while hopeful, urged caution and insisted the chances were no better than “50-50”.
If given the go-ahead, the track would be constructed in the current showring and may only take eight weeks to build.
Mr Harkess said: “We have met their representatives twice now and they have taken on board the information we have given them.
“They have a list of what we would require to be at Ingliston. They have never been negative and are very friendly, but they have never agreed to us staging speedway either.
“Ingliston is no different from any other business – they need to maximise the use of their facilities.”
If Monarchs, who are believed to pay the highest stadium rental in the sport’s Premier League, are given the go-ahead, work to install a new track would begin in October.
Mr Harkess said: “We are at Armadale until that date and we have no plans to do anything, anywhere, until then.
“If Ingliston say yes, I don’t think they would be too keen on us doing any work there and not giving them any rent until next March.”
He added: “It would be bigger than our Armadale circuit and we could have it installed within eight weeks. We would also have to provide floodlights, build a safety fence, plus construct a pits area.
“Ingliston has a lot of plus points, a good catchment area and I’m sure we could attract more fans from Edinburgh.”
A spokesman for the Royal Highland & Agricultural Society of Scotland (RHASS), which operates the showground, said: “We are looking at the options and working with Edinburgh Monarchs to make sure we understand their requirements.”
He said RHASS chief executive Stephen Hutt and another member of the management team had visited Armadale and was planning to visit showgrounds in England to see how speedway worked there.
OLD SKIDS ON THE BLOCK
THE first speedway meeting in Edinburgh took place on May 19, 1928 at Marine Gardens in Portobello in front of 10,000 spectators.
After the Second World War, a new track was built at Old Meadowbank. The Monarchs took part in their first fixture in 1948 in Bristol.
The Monarchs moved to Coatbridge for a spell before returning to the Capital’s Powderhall in 1977.
They remained there for 19 seasons until the stadium was sold, before moving to Shawfield in Glasgow and then making Armadale their home in 1997.