Maguire was reportedly the subject of a £70-million bid from Manchester United earlier this month, and Manchester City are also believed to be interested. The 26-year-old has apparently told Leicester he wants to join either Manchester club.
"Harry's a top-quality player and no one has come near the valuation to tempt the club to sell," Rodgers told BBC Sport after the English international featured in Tuesday's 1-0 friendly defeat of Scunthorpe United.
"The other club interested is a huge club, but he's a really good guy," Rodgers added. "I've been in this position a number of times and it's never easy but he's taken part in everything and hasn't showed anything other than sheer professionalism.
"You've seen that tonight with the 45 minutes he played."
Maguire went from Hull City to Leicester for around £17 million two summers ago. He's lauded for his bustling runs from defense and aerial ability, and both qualities were center stage when the Yorkshireman starred throughout England's 2018 World Cup campaign.
The Sheffield United product subsequently appeared 31 times in the 2018-19 Premier League season, leading center-backs in completed dribbles (17) and finishing third behind Sean Morrison and David Luiz in short-range key passes (10).