That was the message from the pair's former team-mate Darren Huckerby today as the end of Craig Levein's wretched time in charge drew nearer.
Huckerby played alongside the duo during his successful spell at Coventry City back in the 1990s and reckons they would be the perfect men to take charge of Scotland and lead the country forward.
"I would like to see Gordon back involved in football and Gary, too, and if they were to get a job together I think it would be a very fruitful partnership," he said.
The Tartan Army would almost certainly welcome the appointment of two individuals who attained hero status during their glittering international careers.
Strachan was a firm fans' favourite in his heyday and won 50 caps. Memorably, he scored against West Germany in the World Cup finals in Mexico in 1986.
McAllister, meanwhile, represented Scotland 57 times and played in the European Championship finals in 1992 skippered the Dark Blues at Euro 96.
Since hanging up their boots, Strachan has managed at Coventry, Southampton, Celtic and Middlesbrough, while McAllister has had stints in charge of Coventry, Leeds United and Aston Villa.
Under Strachan's expert eye, Huckerby developed hugely as a player before he eventually joined Leeds for a £6million transfer fee in 1999.
He recalled: "I enjoyed my time at Coventry both working under and playing with Gordon.
"He had vast experience of the game and great ability. He was a good tactician and a great motivator.
"What I really liked about Gordon was that he wanted me to be a better player. He was a very important man in my progression as a professional footballer."
However, Huckerby reckons the Scottish game needs to undergo a revolution before Strachan and McAllister could lead the national team back to a major tournament.
"Bringing in a new boss is not the solution to Scotland's problems in my opinion," the former striker commented.
Levein is set to be sacked as Scotland manager following the latest poor results in his disappointing tenure.
Defeat to Wales last Friday night and again to Belgium on Tuesday evening have killed off our already slim hopes of making it to the World Cup finals in Brazil in 2014.
The SFA board, including chief executive Stewart Regan and president Campbell Ogilvie, will discuss his future in the coming days – but there looks set to be just one outcome to their deliberations.
Huckerby, though, has sympathy with Levein as he believes Scotland no longer produces the calibre of player needed to scale the heights they once did on a regular basis.
And he has questioned whether Strachan, despite being out of management for two years, and McAllister, who has not worked in football since last summer, would take the arduous job on.
"The Scotland position is going to be a tough ask for whoever comes in and takes over if the SFA decide that a new manager is, indeed, what is required," reflected the ex-Norwich City man.
"Scotland do not have the players they once did. They do not have a pool of talent like, say, England have that is required to get a country to the finals of a major tournament.
"I think there are bigger issues in Scottish football that need to be addressed.
"The SPL, for instance, is nowhere near as strong as it once was with Rangers dropping down to the bottom division. That surely has to have an impact on the quality of player.
"I think a big overhaul of the game is Scotland is required before the national team's results are going to improve.
"It is not just down to the manager. The whole football culture has to change."
Huckerby continued: "If Gordon and Gary were to come in and take over what can they realistically achieve? Qualification for the finals of a major tournament once in a while?
"It is debatable Scotland could even achieve that with the players they currently have available to them.
"Put it this way, it is not a job any Barclays Premier League managers will be looking to get. It is a big job and a lot of things need to be changed off the field before success can be achieved on it.
"Is Gordon really going to be interested in taking on a job that would be that difficult?
"Is he going to be interested in a job where all he can do is move the team up the rankings? I'm not sure."
Yet, Huckerby believes Scotland can still upset their odds after seeing the national team led by another of his former team-mates stun European football this week.
The Northern Ireland team managed by his old Coventry comrade Michael O'Neill drew 1-1 with Portugal in a World Cup qualifier in Porto on Tuesday evening.
"Northern Ireland did very well to get a point away from home against a country like Portugal," he agreed. "It was a great result for them. It shows it can be done."
