"I think we can keep both players", said Puel, after City suffered a 2-1 defeat to Udinese in Austria.
Puel is determined not to lose Maguire ahead of the Premier League opener with United next week.
As a rare breed of ball-playing English central defenders, the robust Foxes star impressed with England during their run to the semi-final of 2018.
However, Maguire won't force a move from Leicester and is waiting for the two clubs to reach an agreement.
One player who could sign is Barcelona bulldozer Yerry Mina, whose stock has risen after a fine World Cup in Russian Federation.
"If we have another surprise before the end of the pre-season, it will be tough".
"We can not lose players just a few days before the beginning of the season".
"He was great and played very well. It was not a surprise to see him perform well at this level in the global game. To change the scene before the start of the season is not possible", Puel added.
United manager José Mourinho has been unhappy with how the club's transfer business has progressed over the summer, and has identified Maguire as a potential target to bolster his defence. He [Maguire] can continue to perform with Leicester and improve and that is the important thing always with a young player.
Leicester will hope to have both players in the ranks when they travel to Old Trafford for the opening match of the Premier League season on August 10. "In every preseason it happens the same with every club which is the manager wants more".
Harry definitely had an outstanding World Cup and looks the part but it would be a stretch to say he fits all three characteristics simultaneously. Its sole preseason win came against AC Milan last week.