Barrow took over as assistant manager to Gary Caldwell at the League Two outfit before the start of the season.
But Caldwell was sacked yesterday after the Spireites went down to a 2-1 home loss to Accrington Stanley that left them second from bottom.
Chesterfield, according to director Ashley Carson, wanted Barrow to take temporary charge while the club begins its search for a new boss.
But reportedly the 63-year-old turned down the chance out of loyalty to Caldwell, with whom he had previously worked with at Wigan Athletic.
Carson told the Derbyshire Times: “I had hoped that Graham Barrow would take over as an interim but Graham has made it clear that he came here to support Gary and if Gary goes, he goes.
“Is he resigning or isn’t he? That’s the question. He’s said he’s not so he’ll either have to work his two months notice or there will be something done.
“He’s made his decision not to assist so we’ve got to sit down and see what the way forward is, over the weekend.”
Later last night it was reported that the Spireites have subsequently appointed the club's director of recruitment and development, Guy Branston, as caretaker manager.
With Carson adding: “I offered the role on a temporary basis to Graham Barrow, but he flatly refused. He came in with Gary and he didn’t want to take it.
“Guy is going to take control in the short-term and Matt Duke (goalkeeping coach) will help him out.”
Before his sacking Caldwell had insisted that Barrow was 'fully committed' to Chesterfield after he was strongly linked to the vacant position at the club he stills holds dear to his heart.
But the Chester City legend had not publicly ruled himself out of the running to become Jon McCarthy’s replacement before the deadline for applications closed last Wednesday.
The Blues will interview candidates on Monday and Tuesday with a view to making an appointment before the home clash Maidenhead United on Saturday.