The SFA sacked Craig Levein on November 5 after almost three years at the helm of the Tartan Army. The decision came as a result of a poor run of results which saw the Scots win just three of their last 12 competitive internationals.
Fletcher was handed his Scotland debut in 2003 by Berti Vogts and has since gone on to gain 60 caps, playing for a further four managers at International level. And the Manchester United midfielder has stressed the need for the SFA to appoint a manager with a long-term vision for the national side.
He told reporters: "If it could happen before Estonia then that would obviously be beneficial because a friendly game in preparation before a qualifier is always ideal.
"A new manager taking over as soon as possible is always ideal. But if it means taking a bit more time to get the right choice looking at it long term, and then take as much time as they need.
"Maybe there are a lot of candidates and for whatever reason it takes time, the most important thing is getting the right man who can provide a bit of continuity and take Scotland forward not just for the next couple of years but hopefully five or six years and really stamp his authority and take the country places where we want to go."
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He added: "We are all disappointed Craig left, I think all the players would have liked to have seen him stay and continue his work and hopefully it could have come through on the pitch, but ultimately that's not the case."
"Just now we are working with a really experienced man in Billy Stark, who has been fantastic in the few days we have been together. He is desperate to do well and desperate to get a win.
"Although I don't think he will be expecting to be named a new manager, he will be desperate to get a good result and who knows what could happen.
"He has done great things from the Under-21s and got a lot of respect from all the players and even in the couple of days that he has been in charge, a lot of players have been very impressed by him.
"If Billy could get a good victory and there is not a manager appointed before the next game, and we get another good victory against Estonia, then he really throws his name into the hat.
"It would be a choice backed by me but I'm not here to pick managers, I'm here to play for my country whoever is in charge and give them 100 per cent commitment whoever the SFA decide to pick."