The 19-year-old is second choice to regular Dons number one Seb Brown but had been promised a run-out at Underhill, only to suffer a knee injury during the warm-up prior to last weekend's clash with Torquay.
However, manager Terry Brown now expects Turner to be available.
"We promised Jack a home and away match before the end of the season," said Brown.
"He has had the home one and I would like to get him in for the Barnet game if I can. He is a quality young goalkeeper who deserves it as he has been on the bench all season. I know he will not let us down if he comes in.
"The physio is saying that he is 50/50 to play, but I spoke to Jack and he is saying he is 100 per cent going to make it so I expect he will be fit."