There are only nine Masters events and four - Indian Wells, Miami, Canada and Cincinnati - are in North America. The others are in Monte Carlo, Rome, Hamburg, Stuttgart and Paris Bercy.
Indianapolis tournament director Rob MacGill said they have told the men's tennis tour (ATP) they are interested in a more elite status.
To get Tennis Masters Series (TMS) status, Indianapolis would need to take over an existing slot and prize money would have to be increased from $800,000 (?878,000) to about $2.95m (?3.2m).
Australia's Pat Rafter, who won the Indianapolis event last week, favours such a move. He said: "I'm sure this one (tournament) could accommodate it (Masters status).
"There are enough courts... there's a good atmosphere and there's a good crowd. It's a good tennis knowledge crowd."
However, none of the current North American Masters Series events are likely to give up their status.
The one TMS-sanctioned event believed to be considering giving up that distinction is Stuttgart.
But the German tournament is in mid-October - the middle of the European indoor season - and those dates would not appeal to the Indianapolis organisers.
Hong Kong, whose tournament runs from September 24 to 29, has been linked with that slot if it becomes available.
Reuters
Organisers of the Indianapolis Championships want to bump the men's tournament up to Masters Series level - just one below Grand Slam status.
