GALLERY: Wimbledon men's final: Roger Federer v Andy Murray
VIDEO: Andy Murray's tearful post-match interview
Federer says on Monday he might give the honour to someone else.
The 17-time Grand Slam champion was the Swiss flag-bearer at two other Summer Games.
He teamed with Stanislas Wawrinka to win a gold medal in doubles at the 2008 Beijing Olympics.
Speaking a day after winning his record-tying seventh Wimbledon title, Federer says an announcement on the flag choice could come "in the next 10 days or so."
The opening ceremony is on July 27. The Olympic tennis competition, which is being held at the All England Club, starts the following day.