Brendan Rodgers insisted Leicester City would not be selling Wesley Fofana to Chelsea and derided Newcastle United's reported offer for James Maddison.
Leicester are the only Premier League club yet to make a new signing with less than a week to go before the start of the season.
With finances said to be tight at the King Power Stadium, a number of key players appear to be of interest to rival clubs.
Chelsea are reportedly considering a move for centre-back Fofana, having lost Antonio Rudiger to Real Madrid and Andreas Christensen to Barcelona while missing out on top targets Matthijs de Ligt to Bayern Munich and Jules Kounde also to Barca.
Reports suggest Leicester would only countenance the sale of one of Fofana or Maddison, and Rodgers ruled out the possibility of his top defender departing.
"Naturally, he's a top talent," Rodgers said following Sunday's 1-0 friendly win over Sevilla. "He's not for sale.
"He still has lots of improvements to make. He's very happy here, he really enjoys being here.
"Naturally, he will attract the interest of other clubs. Our job, in not signing anyone so far, is to at least keep the players we have. I know that's the intention of the club."
Rodgers was slightly less firm on Maddison's future, although he suggested the £40million fee Newcastle were said to be willing to pay fell well short of the midfielder's value.
Newcastle have also been linked to Maddison's team-mates Youri Tielemans and Harvey Barnes, while they last season targeted Rodgers himself before appointing Eddie Howe.
"He's still very much a player here," Rodgers said of Maddison. "Naturally, the players are sought after because they are talents.
"You see his performance, you see how happy he is, and he's not a player we want to sell.
"It's not for me to put valuations on the players, it's not my side, but [£40m] might just cover three-quarters of his left leg, that price. He's a top player."
Another player who could leave Leicester is captain Kasper Schmeichel, who has held talks with Nice.
Lucien Favre, coach of the Ligue 1 club, said over the weekend a potential move was "a real lead" but "not yet done".
Rodgers added: "There's been a little bit of interest over the summer.
"Kasper has earned the right to have a think about the next chapter of his career and where that's going to be. When there's something concrete, we'll sit and discuss it and take it from there."