Vale are seven points outside the top six with three games left, but Alnwick says adding to his 13 shut-outs this season is a good target to aim for.
"We want to win every game and see where we finish," Alnwick, 22, told BBC Radio Stoke.
"Hopefully we can win all of them with clean sheets."
Twelfth-placed Vale have won their last two games - including the team they are chasing in sixth place, Gillingham - without conceding.
However, they need to win all of their remaining matches and hope for an unlikely set of results to go their way if they are to sneak into the promotion picture.
"We're disappointed we're not right in the mix coming into the last few games," Alnwick said.
"Our defensive record has been good all year - personally I'm happy with the way things have gone, people were putting us as favourites to go down but we've had a good season."
Vale boss Rob Page may choose to stick with the 3-5-2 formation that proved so effective in their 2-0 win at Gillingham, in Saturday's home game against another side chasing a top-six finish, Rochdale.
"The manager threw it at us as he wanted to match Gillingham up," he said.
"I think it was tactically very well done, the lads liked it."
Goalkeeper Jak Alnwick is determined to finish the season with three more clean sheets as Port Vale chase an unlikely play-off place in League One.