The two sides meet in the fourth round of the FA Cup, with Liverpool firm favourites to progress at the expense of their Sky Bet Championship hosts.
Howe, 36, has drawn plaudits for the way he sets his team out to play and the former Burnley boss has revealed spending time with Rodgers has helped him build his own philosophy.
"Brendan inspires me," said Howe.
"I have known him for a while and have been very fortunate to have the opportunity to watch him work and to build a relationship with him.
"He is definitely one of my role models, someone I look up to. He is an innovator, a real thinker and gets his team to be brave and play brilliant football and deserves all the success he gets - I hope he goes on and does well for Liverpool long-term."
Rodgers' Liverpool sit fourth in the Barclays Premier League as they seek Champions League qualification.
And Howe is hopeful the meeting with Champions League-calibre opponents Real Madrid, who ran out 6-0 winners in a pre-season friendly against the Cherries, can help his players deal with facing such an established club.
"It is an opportunity that doesn't come around too often, the chance to pit your wits against one of the best managers in the country and some of the best players in the world," Howe said.
"We had it against Real Madrid in a pre-season friendly but they are nothing like FA Cup matches so in that respect they are very different.
"They gave us a football lesson, we were in the game for 20 minutes and thought we had started well and then before you know it we were 3-0 down.
"The players we were playing against will hopefully stand us in good stead for this, we know the things we need to improve from that game and we did take a lot out of it so hopefully it will help us.
"I'm pleased that our players have been exposed to games like that previously because they are different and the players have to adapt mentally to it."
Having lost just one of their last six games, Howe is determined Bournemouth keep to his own style and approach.
"We are obviously aware of their strengths and how they play and their main danger men but it is a game where I want our players to express themselves and give a good account of themselves," he said.
"We might lose the game but I want people to go away thinking Bournemouth play good football and they are a very good team."
Rodgers may make wholesale changes, with Merseyside rivals Everton visiting Anfield on Tuesday night.
But if 22-goal forward Luis Suarez is involved, Howe conceded it could be a long afternoon for his defence.
"I don't think you can make too many plans for him," Howe said.
"It is down to the team shape and keeping your organisation right; if you do those things you might have a chance of keeping him quiet.
"But better managers and better players than us have tried to keep him quiet and failed, it is probably the most difficult task in world football at the moment."