Jack played the whole 90 minutes of the under-20s clash with Falkirk, which ended 3-3, while left-back Naysmith was taken off after 60 minutes following a successful comeback.
Naysmith has only played two matches since August after being hit with hamstring and calf injuries while Jack has been out for four months after suffering a broken foot while on Scotland Under-21 duty.
Both could now go into the squad for the Clydesdale Bank Premier League clash with Dundee at Pittodrie.
Jack told RedTV: "I will need to see how I am in the next couple of days but even at the end of the game I still felt fine. If I'm called upon I'll be ready to play.
"It was just good to get out there and get back touching the ball and getting involved and a few tackles as well. I came through it well.
"It started at a really high tempo and when you have been out for three or four months it's hard to get straight back to that tempo. But it all comes back. It will maybe take a couple more games to reach that sharpness."