McAllister hopes to get the site of Cordyce School in Dyce to build his first Assassin Health Centre.
Parkhill Garden Centre and Seasons Coffee Shop has submitted a bid to move to the same site.
The city growth and resources committee were due to discuss the bids on Wednesday.
The decision will now happen on November 29 due to “complications” around the offers.
Parkhill and Lee McAllister goes head to head
Steve Whyte, the council’s director of resources, explains the reasons.
“Until we resolve those issues we wouldn’t be able to give a firm recommendation to the committee.”
McAllister’s plan could transform the site into a sports centre with a swimming pool, cafe, and gym.
Bosses at the garden centre want to move into the site as they claim the salt spray from the AWPR will damage plants. This stops the centre trading over the winter months.
Affordable housing developer First Endeavour LLP has got behind the garden centre plan. It said it would work with them to build 60 homes, community allotments, a care home and medical centre on the site.
Mr McAllister said he was “surprised” the decision is delayed.
He added: “I’d like to see a decision made either way. We could make new plans in a worst-case scenario or in a best case we get on site as soon as possible.
“I was looking to get it built and open by August next year.”
A spokesman from First Endeavour LLP said they had been notified by the council of the delay.
He added: “Our proposals would see 43 jobs saved at the garden centre. We are working very hard to secure a medical facility and doctor’s surgery on the site.”