The Skrill Premier team defeated Cardiff City at Moss Rose at the same stage last season before losing 1-0 at home to eventual winners Wigan in the fourth round.
The tie against managerless Wednesday, who are 21st in the Championship, gives the Silkmen a chance to earn some much needed cash in order to pay off their debts with the winner's receiving £67,000.
Askey, who replaced Steve King as manager in June, told Sky Sports News: "I think it's a good draw for us - the fact that we have been drawn at home against such a big club as Sheffield Wednesday. They are obviously not having the best of times at the moment and they won't relish coming here.
"The FA Cup is massive to smaller clubs and the financial rewards are huge. It's vital to us because we have hit rock bottom this season - the sort of season we are lucky to survive, so any money that we can get in is much needed.
"If we can manage to beat Sheffield Wednesday, that would be a big shot in the arm for survival."
Macclesfield drew a crowd of 2,438 to Moss Rose for their 3-2 victory over fellow non-league side Brackley in the second round and Askey is hoping the locals will turn out in force for the visit of the Owls.
He said: "They are starting to come back and we are starting to become a family club again. We are starting to get a lot more support than we were in the last two or three years so it's good to see and people are enjoying it.
"We are competing with Manchester United and Manchester City and you are never going to compete with them so it's important that we get the young kids involved from the local community and they get behind their town team.
"That's what football clubs are about - they are about community and identity and hopefully the Macclesfield people will get behind us."