By convention, former presidents tend to leave the political fray and avoid commenting on their successors.
Mr Obama said he would give Mr Trump time to outline his vision but added that, as a private citizen, he might speak out on certain issues.
Mr Trump spent the weekend interviewing candidates for top jobs in his cabinet.
"I want to be respectful of the office and give the president-elect an opportunity to put forward his platform and his arguments without somebody popping off," Mr Obama said at a forum in Lima, Peru.