The SFA were faced with a cost of around £1million to bring the South Americans to Scotland in November which would have meant increased ticket prices.
SFA chief executive Gordon Smith took the unusual step of canvassing the Tartan Army on the viability of going ahead with the game
"Since we started the debate on the proposed Argentina game last week we have been inundated with calls, letters and emails from Scotland fans," Smith said.
'Hundreds of people have taken the time to get in touch with us and give us their views and I thank them for doing so. This has been a fascinating debate about an important issue.
"The vast majority of people who got in touch with us were clear that they want Scotland to continue to improve and to regularly qualify for World Cups and European Championships.
"They understood that we do this by playing against better players and against different styles of teams. However, despite the support for the idea of playing Argentina, most of the people who spoke to us also told us that there were issues around paying a premium price for a midweek match at that time of year.
"This is why we have decided to cease negotiations with the agents who represent Argentina and are now involved in discussions with other countries about playing at Hampden in November.
"I firmly believe that consulting with the people who would be paying their hard earned money to watch this match was the right thing to do on this occasion.
'The range of views that we have received have all had one common thread - everyone wants to do what is best for Scotland.
"Once again, I would like to thank everyone who took the time to get in touch with us. I will always take decisions which I believe are good for Scottish football.
"However, when I think it is the right thing to do I will canvass opinions and speak to our supporters.
"Doing so is healthy for our game."