It was initially feared that Faletau, 24, had suffered another setback to his left ankle - an area in which he has previously required surgery - after he limped off in the Dragons' pre-Christmas GUINNESS PRO12 victory over Zebre.
But despite sitting out of the Boxing Day win against Cardiff Blues, the back-row forward could be back in the starting XV to help his side do the double over their Welsh rivals on New Year's Day.
However, Jones admits it is an injury that will require monitoring.
"It seems he tweaked an ankle. The specialist he saw said it was nothing major and for 'Toby' to see how it goes," Jones told Wales Online.
"Sometimes there's a rush for players to have surgery but it was decided to wait for it to settle down.
"Toby has trained. He's done some running on it under the guidance of our medical staff and conditioning team. We haven't ruled him out of the New Year's Day derby with Cardiff Blues at Rodney Parade."
The Dragons are one of the form teams in the GUINNESS PRO12 after adding to their one win in nine games with back-to-back victories in the last two weeks.
And should another win come on Thursday, they will jump ahead of the Blues in the table - but Jones has warned his side it will not come easy.
"We just want to beat the Blues again. The Blues will have been disappointed with that result against us but
they are starting to take shape under a new coaching set-up," added Jones.
"It's pretty simple, if we win our games we will move up the table. We want to finish as high up the league as we can because we don't want to finish the season as the bottom Welsh region."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland