Graham Construction is due to deliver the two new health facilities after years of consultation and working up final designs.
Graham started enabling works last November, which were completed this July and is now awaiting final sign off of its final price.
But the firm’s final projected building cost has soared above the original £164m budget, with the price now reported by the BBC to be over £200m.
This has prompted the trust to launch an independent review into the cost of the project and raised the prospect of further design changes to bring the project into line with original budgets.
A spokesperson for NHS Grampian said: “The analysis of the tenders for the main construction works is underway.
“The tendered costs that have been returned are higher than estimated at the outline business case stage, reflecting the challenges within the construction sector and the wider uncertainty regarding Brexit and the economic position.
“We have commissioned an independent review of the project costs, and are also using the opportunity to review the design of the facilities in light of the learning from the projects in Glasgow and Lothian.
“NHS Grampian is fully committed to the project and continues to have the full support of the Scottish Government.”
The project involves two new buildings, which are due to be opened on the site in 2021.
The Baird Family Hospital will be around 26,000m² in size, while the ANCHOR Centre for cancer treatment will be around 5,600m² in size.