Cole caused controversy at the weekend when he accused the England captain of being the national team's "supposed golden boy" and insisted any other player would have been dropped if they had gone through a similar dip in form.
But Southgate yesterday maintained the outburst would be overlooked by the England coach, Kevin Keegan, when he names his party today for the two games with the Scots.
"It's up to the manager to pick the squad that he thinks will do the job," explained Southgate, who played when England beat Scotland 2-0 in the Euro 96 finals at Wembley.
"If he feels Andy is good enough to be there, I'm sure he won't be too concerned about what's been said. He'll pick his team on merit, though I've only read what's been quoted in the newspapers and I haven't read it in full context."
England and Scotland have been left vying for one Euro 2000 spot by their failure to finish top of their qualifying groups. "We've both got a lifeline," Southgate said, "and it's up to us to take the chance.
"Everybody involved with England would hold their hands up and admit the qualifying run has been very disappointing, right from the first game.
"I think both sides have been criticised in the last few months and both sides would be the first to admit they could have played better in their group games.
"But it's come to this and it'll be a great fixture. I think it's going to be very tight because both sides know each other so well. There's no question there will be little to choose between the teams. It'll be like a domestic cup tie, if anything. I don't think home advantage will have a great bearing on it because you're not travelling thousands of miles and worrying about the food or hotels.
"The rest of Europe is probably laughing at how much publicity and hype is surrounding the fixture because for them some of the Champions' League games have been bigger. But with the rivalry that exists between the two countries, that will always be the case."
The former Manchester United and Republic of Ireland striker Frank Stapleton also believes that Cole should play for England. "I can understand the player's frustrations and he's not really had a good run with England," Stapleton said.
"He's been in and out of the team, while the changes in management have not helped. But if someone is scoring goals like he is, then you can't ignore him. After all he has not fallen out with Kevin Keegan and certainly on current form and goalscoring he should be included."
Keegan could risk creating a bad atmosphere in the England squad if he includes Cole and Shearer, but Stapleton believes that can be avoided.
"I think everyone has to concentrate on the football side and remember what's at stake," he said. "The manager has got to sort out any problem there could be before the players step out on to the training pitch.
"There has got to be unity within the squad and if necessary the manager should have clear-the-air talks.
"There is a huge prize at stake for the winners of this play-off and they have to work together to achieve it."