Maddison's future continues to dominate headlines, with the Leicester star reportedly a top transfer target for Premier League giant United.
United is set to try to prise Maddison to Old Trafford at the end of the season, however, Rodgers hopes the England international midfielder's long-term future is at King Power Stadium.
"Talks have been ongoing with the club and his representatives," Rodgers said. "I know the boy is very happy, he wants to be here and he sees this as the club he can develop at. I am hopeful it will be done."
Maddison has scored nine goals across all competitions for Leicester this season, six of those coming in the Premier League with three assists.
The 23 year-old has established himself as one of the Premier League's best attacking midfielders since joining from Norwich in June 2018.
Maddison has enjoyed another fine campaign as Leicester sit third in the standings and on track to qualify for the Champions League after 27 matches.