The extent of Byrne's ankle injury led to suggestions that he may be forced to spend a lengthy spell on the sidelines but, with a medical assessment taking place today, the prognosis is expected to be better than at first thought.
"Lee's condition is much more comfortable and he is able to take weight through the ankle," said Ospreys physio Chris Towers.
"He will be assessed jointly by the Ospreys and Wales medical teams today and will have a scan if deemed necessary.
"The initial signs of recovery are very positive suggesting the injury may not be as severe as initially feared, and we're hopeful if he continues to improve over the next couple of days, he could still be available to face Leicester next weekend."
Currently rated as in the in-form full back in world rugby, Byrne's absence would be a major blow for the Ospreys, Wales and, possibly, the Lions, but the former Scarlet was in a more positive frame of mind on Sunday night.
"It seems like I twisted it but we will have to wait and see. It doesn't feel too bad and isn't as painful as when it happened."