Swindon hope to name Southampton academy director Dave Hockaday or his Newcastle counterpart Richard Money as manager, BBC Radio Swindon understands.
Reports have suggested former Walsall boss Money has already left his post at St James' Park.
Dave Byrne has been in caretaker charge of the Robins since the departure of Maurice Malpas on 14 November.
Town have refused to comment on these claims but hope to name the new boss in time for Saturday's game with Yeovil.
The club said earlier on Thursday they are confident they have got the right man, but admit he may not have the 'wow' factor of some of the people they have talked to.
Chief executive Nick Watkins told BBC Radio Swindon the man in question has got all the qualities they looked for.
"It isn't just the wow factor. It isn't just a name. It's someone who's got integrity, man management, ability to motivate and inspire," he said.
"They've got enthusiam, energy and real self-belief in their ability to deliver success."
Gary Speed, Colin Calderwood, Ian Holloway and Steve Cotterill have all been linked with the job since the departure of Malpas.
Swindon have given no indication of who the new man is, but Watkins said they are looking at the job as a long-term role.
"They see Swindon not as just a staging post onto their next appointment," he said.
"They see Swindon as being their opportunity to take this club back to where it belongs."
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