Watson, who won four of his five British Open titles in Scotland, played four times in the biennial team tournament and captained the 1993 US team to victory at the Belfry - the last time the Americans won in Europe.
"It would be cool to be Ryder Cup captain again," the 63-year-old said after his final round at the Australian Open.
"I hope so, I hope so. It would be a great honour if I got tapped on the shoulder. I know that '93 was the last time I've been to a Ryder Cup. I'd like to go back as captain. That would be cool."
The US has not had a repeat captain since Jack Nicklaus got the nod for a second time in 1987.
Europe will go into the 2014 version of the event as holders having staged a remarkable final-day comeback to beat Davis Love III's US team 14 1/2 points to 13 1/2 at Medinah earlier this year.