The 19-year-old has burst onto the scene in 2012/13, graduating out of the Whites' famed academy system to become a first-team regular.
Premier League eyes are said to be monitoring his progress, with talk of summer bids intensifying as the re-opening of the transfer window edges ever closer.
Leeds are, however, determined to keep Byram on their books, with McDermott having succeeded Neil Warnock with the intention of retaining key men and strengthening where required.
He told Sky Sports News HD: "He will get better and he will improve at Leeds, there is no doubt about that.
"He's a Leeds boy - the fans love him, the staff love him, the players love him.
"From our point of view, my point of view, absolutely, 100 per cent, I would expect Sam to be playing for us next season."
Byram has also hinted that he will be a Leeds player in 2013/14, with the promising full-back aware of reported interest in his services, but reading little into it.
He said: "I'm really happy playing here. I've played quite a few games, which I'm pleased with.
"I'm learning here and the best way to learn is by playing. While the new manager is here, he has got great ideas and is really encouraging.
"It's quite encouraging to know that people are interested. But, like I say, I'm happy here. I'm enjoying my time playing for Leeds and I'm hoping that continues."