The 67,800-seater stadium – the largest in the country – is one venue being considered, alongside the three major football grounds in Glasgow.
Matches have been taking place in London for several years, with bosses now looking to expand to other parts of the UK.
It’s estimated that hosting a match at Murrayfield could be worth £25 million to the Capital’s economy.
John Donnelly, chief executive of Marketing Edinburgh, believes the city would be an ideal host.
He said: “Murrayfield Stadium is embraced by the whole nation as the home of key national sporting events, with tournaments such as Six Nations Ruby Union typically generating £52m per year for Scotland.
“Given the rising popularity of NLF in Scotland, which is increasingly moving from cult to mainstream following, there is a huge opportunity for the city to further build on its successful sport tourism
“Added to the fact that Murrayfield was the historic venue of the NFL’s Scottish Claymores, it seems right that Edinburgh becomes the home of any new sporting fixture for Scotland.”
Murrayfield hosted 26 matches featuring the now defunct Scottish Claymores in the old European NFL league.
The Scottish Rugby Union admitted it was open to the prospect of top American teams playing there.
They said: “We are very open to welcoming NFL to BT Murrayfield and building on our strong history of hosting American Football games at the stadium.”
Fans would flock to the ground for the experience, said Edinburgh Wolves player and coach Lloyd Dignan.
He said: “The games at Wembley and Twickenham sell out completely and there’s no reason why they wouldn’t be able to fill Murrayfield.
“It is also an easy and natural transition from a rugby pitch to an American football pitch. Scotland would love to see something like this and fans from across the UK would travel to Edinburgh
“The airport is only about ten minutes’ journey from the stadium which is used to hosting massive events.
“Edinburgh has got to be one of the best locations in the UK for an event like this.”
Amateur team the Edinburgh Wolves, launched in 2002, play at Meggetland and were recently promoted to the top division in the British American Football Association.
The popularity of the sport has grown in the city over the past ten years despite the collapse of the Scottish Claymores, who played successfully in the NFL Europe, predominantly at Murrayfield Stadium, until league bosses discontinued the team and they were later replaced by the Hamburg Sea Devils in 2005.