Police Scotland named the men as Craig Munro, 30, and 26-year-old Allan Robertson.
One image appears to have been taken at the same location where missing mother Farrah Fadli was sighted earlier this month.
Police Scotland and the Crown Office said they were unable to confirm if the investigations were linked.
A spokesman for the Crown Office said it was also unable to say, for legal reasons, why the two men were being sought.
Ms Fadli, who is also known as Farrah Gillespie, has been missing from her home in Ayr since Wednesday 12 October.
The 29-year-old initially disappeared with her children but dropped them off at a friend's house in Irvine on 14 October. She has not been seen since.
Ms Fadli is 5ft 4in, of slim build with dyed blonde hair.
She has not gone missing before and officers have said previously it is extremely unusual for her to leave her children for such a long time and not be in touch with her family and friends.
Police have released CCTV images of two men they are trying to trace and have warned the public not to approach them.