The German club's sporting director, Ralf Rangnick, said he had no interest in selling any of the first-team players.
Liverpool have been linked with a summer move for midfielder Keita, while Arsenal boss Arsene Wenger is understood to be admirer of playmaker Forsberg.
RB Leipzig are preparing for their first ever Champions League campaign after finishing runner-up to Bayern Munich in the Bundesliga last season.
"We're not thinking about selling our best players this summer," Rangnick was quoted as saying by the Daily Mirror.
"There's no red line for us. We will keep our team and improve it in several positions."
Forsberg's agent said in May that "big clubs" were interested in the Sweden international and that he could be tempted to leave Germany in search of a bigger challenge.
"I will not comment on the clubs involved. There are big clubs who are very interested in Emil," Hasan Cetinkaya was reported as saying.
"He has made history in Germany. Of course, you know RB want to keep Emil, you need to constantly make sure to make Emil satisfied.
"He has paid back the club ten-fold. Maybe it's time to test himself at a big club."
But Rangnick laughed off the prospect of Forsberg leaving RB Leipzig in the summer transfer window as a "Christmas wish".
"We have amended Emil's contract twice and we cannot do more than what we have done... giving him a contract that runs until 2022," he said.
Meanwhile, RB Leipzig are close to completing a deal for Galatasaray winger Bruma for a fee of around €15m (£13m).
"The player has flown with me to Leipzig," said Rangnick. "We wanted him to look around the city and our training ground before signing."