Herald Sport understands that the Irishman is in talks with Paul Lambert about joining the Midlands club. These discussions started before Keane was contacted by Dermot Desmond, the majority shareholder at Celtic, over the post vacated by Neil Lennon.
Lambert initially believed Keane would take the Celtic job but now expects the former Manchester United captain to take up the chance of working again in the Barclays Premier League and for it to be rubber-stamped this week after Villa sacked former assistant Ian Culverhouse last month..
Working with Lambert, Keane will be allowed to continue his duties as Republic of Ireland No.2 to Martin O'Neill and may also be able to accommodate his role as ITV's top pundit for Champions League nights.
It is highly unlikely he would have been able to continue with either role had he moved back to Celtic.
The developments on a dramatic day have left Steve Clarke, the former West Bromwich Albion manager, as the favourite for the job at Celtic though Malky Mackay, the former Cardiff City manager, also has strong backers.
Oscar Garcia, the former Brighton and Hove Albion manager who was also linked with the post, has taken up a position at Maccabi Tel Aviv.
This left Clarke, the 50-year-old former Liverpool and Chelsea coach, as the front runner with bookmakers but sources last night indicated that the race for the job still had some distance to run.
It is believed Celtic have spoken to Clarke, who has been linked with the vacant Brighton job, and the former St Mirren player has indicated he would be interested. Clarke, who has a particularly impressive pedigree as a coach with Jose Mourinho at Chelsea, is seriously considering working as a coach in his homeland for the first time but Mackay, too, is thought to be a strong contender.
However, Celtic have consistently stated that there were several candidates for the position and a quick resolution is some way off.
Keane's decision to call off talks was announced yesterday morning. Celtic sources contest the assertion that the Irishman was ever offered the job but admitted last night he had asked not to be considered for the position.
Ireland fly out to the United States for friendlies against Costa Rica and Portugal tomorrow and the Football Association of Ireland said: "Roy Keane has confirmed he will travel to the US after deciding not to pursue talks with Celtic any further."
With Garcia and Henrik Larsson, the manager of Swedish side Falkenberg, now unavailable, the leading contenders are thought to be Clarke and Mackay with Owen Coyle, the former Wigan Athletic and Bolton Wanderers manager, also in the frame. However, Keane had been expected to take the role after talks with Desmond, who brokered the 41-year-old's appointment as assistant coach to O'Neill, had approached him last week.
But the Irishman had agonised over the decision to the return to the club he played briefly for in 2006, before instead opting for the role in the Midlands that will allow him to continue in his job with the national team and as a television pundit. The former Sunderland and Ipswich manager analyses matches for ITV and will be part of their team for the World Cup.
He said last month: "I've got a job - I've got two jobs - I can't have another one. They are a brilliant club, an absolutely fantastic football club, one of the best in the world. But I have got a job." He added with a smile: "I'm not taking a pay cut for anybody."
The search for a manager thus goes on with Celtic players returning to training on June 24 before a Champions League campaign beginning on July 15-16. Celtic will also face Dynamo Dresden, who have been relegated to Germany's third tier, in a friendly at the Glucksgas Stadium on July 19. St Pauli will likewise provide warm-up opposition in Hamburg on Saturday, July 26.
Meanwhile, the pitch at Murrayfield will be ready in time for Celtic's opening Champions League qualifiers, according to the company which is installing the new surface. Desso Sports Systems began stitching the artificial fibres into the ground last month but have had to pause as the Edinburgh stadium will host a One Direction concert this evening. The work being carried out on the pitch is a result of a parasitic roundworm eating away at the roots of the old pitch.
Celtic are due to play their initial European matches at the stadium as Celtic Park is being used for events at the Commonwealth Games. The contractors are scheduled to return to work early next week to begin seeding the new surface and remain confident the process will be completed in time for the pitch to settle before Celtic's vital qualifiers.