The Royal & Ancient Golf Club organises the competition and its chief executive Peter Dawson said it will consider taking the competition away from the public service broadcaster if it continues to downscale its coverage of golf.
The BBC holds the rights to The Open until 2016 but from next year will screen just six days of men's professional golf live a year.
"They (the BBC) know we have got our eye on them. It hasn't just been in golf but with the likes of tennis as well," said Dawson at this year's venue of Royal Lytham & St Annes,
"You have to stay in practice and keep up with advances in technology. You need to be in practice to do it well. We obviously want the Open Championship to be seen by as many people as we can. The BBC know they need to get off the financial plateau they are on with the Open Championship by the next time it comes around. Who knows who will be on the scene then?"
Dawson suggested that ESPN as well as Sky could be an alternative broadcaster of the event.
Dawson also questioned the BBC's policy of having people who made their name in other sports front its golf coverage.
At the recent Masters at Augusta, former England cricket captain Michael Vaughan played a key part in the coverage and made a statistical blunder while interviewing Tiger Woods, while ex-footballer Gary Lineker has also often presented golf.
"It does seem rather unusual," admitted Dawson.
At the moment The Open is considered a 'B' event on the government's list of sporting events that must been shown on free-to-air TV.
That puts it in the same category as events such as the Ashes and the Ryder Cup – competitions that do not have to be broadcast live on free TV but must have highlights featured upon it.
Both the Ashes and the Ryder Cup are currently shown live exclusively on Sky.
Two weeks ago the Grand National was broadcast on the BBC for the last time while it also lost the rights to the BMW PGA Championship at Wentworth and the Scottish Open in July.
A BBC spokesperson said: "The BBC have only recently signed a new deal for The Open golf until 2016. We are completely committed to this event and are looking forward to bringing the Championship to audiences for the next five years."