The trunk road drops from 150m (492ft) to 20m (65ft) as it enters a valley at the Berriedale Braes.
Transport Minister Derek Mackay has confirmed that a number of objections have been received to the initial proposals for the improvements.
Last month, Caithness Chamber of Commerce said it was taking too long to agree a plan of action.
Transport Scotland said it was continuing to progress the design work.
The A9 provides a link to the far north mainland coast and the ferry services at Scrabster, Gills Bay and John O'Groats to Orkney.
A public local inquiry is likely to be held into plans to improve a hairpin bend on the A9 in Caithness.