Puel is determined to keep the 31-year-old goalkeeper at the King Power Stadium ahead of his second year in charge of the Foxes.
Leicester managed a ninth-placed finish last season under Puel. Schmeichel was also the Foxes' goalkeeper during their 2015/16 title-winning season, keeping 14 clean sheets along the way.
Following his side's 4-1 pre-season win over Notts County, Puel said as quoted by Sky Sports: "I am not troubled about this. Of course Kasper is a very important player for us. He had a very strong World Cup. We need Kasper, with his character, his performance and his consistency."
The 56-year-old French manager was then asked whether Leicester had received any offers for Schmeichel, given the ongoing rumours of Chelsea's interest.
He said: "No. There is no problem with this. There is a lot of speculation at this moment, it is normal."
Spoken to Claude Puel after Leicester’s 4-1 win at Notts County. “Not troubled” by reported interest from Chelsea in Kasper Schmeichel. “A valuable player for us...had a strong World Cup. We need Kasper”. Puel says Ward signing not to replace Kasper #LCFC #CFC #SSN— Kirsty Edwards (@KirstyEdwards3) July 21, 2018
Schmeichel will face greater competition for his place in the Leicester goal this season, following the club's £12.5m signing of Wales international Danny Ward from Liverpool.
However, Puel was keen to stress that Ward was not signed to replace the Danish goalkeeper, but rather to offer serious competition in order to improve both keepers' respective games.
He explained: "I think he can bring more competition to the squad and more possibilities. It is a good thing to have competition between players in the squad to develop desire. It gives good focus and concentration."
While Schmeichel is not expected to move this summer, he is known to be a transfer target of Chelsea.
The Blues' main goalkeeper Thibaut Courtois has been linked with a move away to Real Madrid, and the London club are said to be considering Schmeichel as a possible replacement, alongside their former goalkeeper Petr Cech.