Following an accomplished Premier League campaign last season, Maguire's authoritative performances for England at the World Cup won him further admirers.
United are rumoured to be readying a bid that would make the 25-year-old the most expensive defender in football but Puel has sought assurances from the Leicester board that none of his prized assets will be leaving before Thursday's deadline.
"It's a good thing for Leicester to keep our valuable players, like Maguire, [Jamie] Vardy, [Wilfred] Ndidi - all these are very good players for us," he told Sky Sports ahead of Friday's season opener at Old Trafford
"It's important to keep them and have a good ambition for the next season.
"I can understand some speculation about our players because we have good players with good attributes, who are interesting perhaps for the future of other teams.
"But I am happy to keep them and to start, I hope, a great season."
Manchester City made Riyad Mahrez their record signing for £60 million ($78m) last month and Puel insists losing another of his A-listers cannot be on the agenda.
"We lost Riyad Mahrez, who was a very good player for us with the possibility to change the game," he added.
"After Riyad it was important to keep our players and add some good players with good attributes to strengthen the team."