The Premier League champions, along with fellow English sides Manchester City, Chelsea and Arsenal, will discover their fate in this afternoon's draw in Monaco.
In last season's campaign, United were booted out of the competition at the round of 16 stage following a controversial defeat to Real Madrid.
"Champions League draw day is a day you always look forward to," Jones told the club's official website. "It's always exciting to watch it and see the balls being drawn out of the hat. It'll be interesting to see who we get.
"We all know what happened last season. Football can be a cruel game at times, but hopefully we can do well in it again this year and really stamp our mark in the Champions League."