Officers have released CCTV images of Craig Munro, 30, and Allan Robertson, 26, who they are keen to trace.
They have warned people not to approach the men.
One of the images appears to show the same location as a picture of Farrah Fadli – also known as Farrah Gillespie – who disappeared earlier this month.
She went missing from her home in Ayr, South Ayrshire, having taken her children McKenzie Scullion, 10, and Eva Kerr, four, with her when she left on 12 October.
Following a police appeal saying officers were “very concerned” at the 29-year-old’s disappearance from her home in Thornyflat Drive, she dropped the children off at a friend’s house in Irvine on Friday night, 14 October, and the youngsters are now with family. Ms Fadli has not been seen since. It is thought that she may have been in contact with the two men in the CCTV images at some point.
Ms Fadli is described as 5ft 4in, slim and with dyed blonde hair. It is not known what clothes she was wearing at the time she disappeared.
It is understood that police want to speak to Mr Munro and Mr Robertson in connection with the death of John Smith, 52, who was found critically injured at Misk Knowes, in Stevenston, North Ayrshire, on 8 October.
He was taken to Queen Elizabeth University Hospital in Glasgow, where he died on 11 October.
A police spokesman said: “The police are currently pursuing a number of lines of enquiry in relation to tracing these males.
“Members of the public are advised not to approach these males but to contact police immediately on telephone number 101.”
Police are still treating Ms Fadli as a missing person and urged anyone with information about her whereabouts to contact them.
Inspector Jim Hendrie said this week: “It is now almost a week since Farrah has gone missing and as time progresses we remain concerned for her well-being.
“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.
“I would urge anyone who knows where she is to get in touch with police immediately.
“If Farrah herself is seeing these appeals, I would ask her directly to get in touch with police. Your friends, family and children are desperate to have you back safe and well.”