Three Wise Monkeys Climbing, the business behind the project, plans to convert Macintosh Memorial Church near the town's High Street.
It has already managed to raise £30,000 in 23 days through a crowdfunding appeal. However, the appeal reaches its deadline at 17:00 on Wednesday.
If the funding bid is successful, the centre will be opened in stages.
A bouldering wall would be created first, followed by a cafe, then a roped climbing wall and extra bouldering wall training room.
A former church in Fort William could be turned into a climbing centre if £40,000 can be raised by Wednesday.