The South London side's demise was confirmed with a goalless draw against the one team below them in the table, Bolton Wanderers.
Asked if he would remain at The Valley, Riga told BBC Radio London: "It will be the content of the next meeting.
"It depends on the context, how they react to things and how they want to do things in the future. That is the most important thing for me."
Charlton lasted four seasons in the Championship since coming up as League One champions in 2012. Next season will mark 10 years since their last term in the Premier League.