Liverpool progressed to the next round with a 5-1 aggregate victory and will face AS Roma in the semi-finals.
"Unfortunately Raggy felt something muscle-wise. Clyne is probably out. He felt an injury in training the day after the game," Klopp told a news conference.
Forward Roberto Firmino is available for the match despite experiencing discomfort in his neck earlier in the week. "Bobby had a little issue with his neck but should be OK, I think," the German manager added.
Klopp said he was hopeful that midfielder Adam Lallana could return to action before the end of the season after picking up a muscle problem against Crystal Palace last month.
"It will be close. He can come back again. There's no rush because it makes no sense. If Adam is available then we'll see. I don't want to close the door for the season."
Liverpool are third in the table with 67 points, the same as fourth-placed Tottenham Hotspur, but have played one game more than the London side. Bournemouth are 11th in the standings.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
