The in-form front-man has a chequered history when it comes to returning from international commitments on time, having been dropped by Black Cats boss Steve Bruce last month after landing in England only on the eve of a league game.
This time Bruce has laid down the law having made it clear to Jones that there are others in his squad that can take his place, should he not return with due haste.
Jones played only the final 15 minutes of Trinidad & Tobago's World Cup qualifier against Mexico on Wednesday and should be fine physically to figure at the weekend.
Having been booked on an earlier flight this time, Bruce envisages few problems with the striker's arrival in the North East.
No problem"Kenwyne will be getting the earlier flight back," Bruce told the Sunderland Echo.
"I told him that he can't play on Saturday if he doesn't. He will fly back through the night and get into London tomorrow morning, so he's still got to get back up to the North East from there.
"But the earlier flight gets him back over here 12 hours earlier, which at least gives him more chance to recover. I'll have to see how he is when he gets back.
"It doesn't matter whether you've played in a game, played the full 90 minutes or not - if you get straight off a plane from Trinidad then you are not going to be in the best of shape."
PromisingJones has enjoyed a fine start to the season having struck up an intuitive partnership with Darren Bent, with the duo having notched 12 goals between them so far.
Bruce is keen for the partnership to blossom further and knows he must keep Jones firing on all cylinders.
"They have become a good partnership and they have proved that they are a handful for any defence," he said.
"Kenwyne has grasped the nettle just recently and done really well. We have to make sure he stays at it."