After failing to qualify for the World Cup, Gordon Strachan left his role with the Tartan Army, and there has been every indication that temporary replacement Malky Mackay will not continue in the dugout after Scotland's 1-0 defeat to the Netherlands on Thursday.
Lambert has been out of work since leaving Wolverhampton Wanderers in May, but the former Scottish international has acknowledged that he holds an interest in managing his country.
The 48-year-old told BBC Sportsround: "I played for the national team, it is my country, so you do maybe think 'let's have a look'. I wouldn't ignore people. If they ask me to speak to them, I would speak to them, of course.
"Whoever gets it has got a big job on his hands. You are not just there to nurture players. The national team has to qualify for a major tournament. It has been 20 years.
"We can't be thinking we will wait three or four years for these players to develop. Whoever gets that job has to do their utmost to qualify. That is the ultimate bottom line."
Lambert has also been linked with the vacant job at Sunderland.