Byram, 21, on the radar of Premier League clubs since making the first-team breakthrough three seasons ago, is a reported summer target for Everton, Sunderland and Newcastle.
But Rosler, who replaced Neil Redfearn in May, said he was not aware of any official interest in right-sided winger or defender Byram during his short time at Elland Road.
“I don’t know where the rumours come from,” Rosler said.
“Nobody has spoken to us at the football club. There have not been any approaches lately that I’m aware of.
“The speculation, who creates that? It doesn’t mean when somebody sells a player from A to B that one of our players will be first replacement for that player.”
Former Leeds head coach Redfearn felt Byram’s talents were better served higher up the field last season and played him on the right wing.
Midfield trio Lewis Cook, Alex Mowatt and Kalvin Phillips, plus left-back Charlie Taylor, another youngster to have worked his way into the first team after progressing through the club’s academy, will continue to play key roles under Rosler.
“I’ve said before I’m excited about that young group of players,” the former Brentford and Wigan boss added.
“We want to build this football club around them and I’m very very keen to keep, especially the one you mentioned, Sam, to keep him here and work with him.
“In all the talks I’ve had with (owner) Mr Cellino and (executive director) Adam Pearson, we don’t need to sell at the moment.
“We are on an even keel and through the efforts of Mr Cellino we can pay our bills and we don’t need to sell to pay our bills and that’s all that I can say.”