Lincoln City chairman Bob Dorrian hopes to appoint a successor to manager Steve Tilson before their game at Cambridge on Friday week (21 October).
Dorrian told BBC Lincolnshire: "I would hope we have a manager in place, if not in charge, by the end of next week."
Tilson and his assistant Paul Brush were sacked on Monday with the Imps 19th in the Blue Square Bet Premier.
Head of youth Grant Brown is in temporary charge and led Lincoln to a 3-1 victory at Alfreton on Tuesday.
But former Lincoln legends Mick Harford and Steve Thompson have been strongly linked with the job as a managerial duo until the end of the season.
Thompson, who also went on to manage Southend, Sheffield United, Cambridge United and Notts County, was in the Imps' hot seat between November 1990 and May 1993.
Apart from caretaker spells in charge of Nottingham Forest and QPR (twice), Harford has twice had spells as a manager, first at Rotherham in 2005.
He then spent the best part of two years at doomed Luton from January 2008 to October 2009, during which time the Hatters were docked 30 points for breaches of off-field financial regulations and relegated from the Football League.
Lincoln are themselves now finding out the financial constraints following relegation from the League for the second time under Tilson in May - and Dorrian admits that it will have an impact on the search for a new manager.
"In reality," he said, "we have to look for a manager with non-league experience, with non-league contacts and who is cheap.
"I don't think we are in a position financially to poach a manager from another club."