Walker apologised last month after twice breaking quarantine guidelines – once to host a party with two sex workers, and a second time to visit family in Sheffield – but also claimed he was “being harassed” by media.
The Manchester City right-back has not received an England call-up since last summer’s Nations League finals and faces stiff competition in his position from the likes of Trent Alexander-Arnold, Kieran Trippier and Aaron Wan-Bissaka.
Southgate said that he would not judge any player solely on their conduct during lockdown, but added that repeated instances of unprofessionalism and misconduct off-the-pitch will not be ignored either.
“When you are dealing with young men there will always be transgressions and I will never make a decision on somebody based on one mistake or one misjudgment,” Southgate said.
“But equally I don’t miss much and our group of staff don’t miss much and you are constantly judging and assessing people and building a picture of what you are going to be working with.
“We judge on the field and we judge off the field. What is the character? What is the personality? We will be away for a lockdown of 40-60-80 days if we go into a tournament. How are those people going to cope with that? Are they really dedicated enough? Are they professional enough?
“So I am not going to not pick somebody because of something that has happened in this period per se, but we have a picture forming all the time of people’s lives and where they are at and all of those things.”
Southgate would have led England into the European Championships this summer if not for the pandemic, but is still looking to build a professional working culture among his players ahead of the rescheduled tournament next summer.
“Character is important,” he said. “If we are going to be a winning team with all the documentaries I have had time to watch and podcasts I have had time to listen to, it is keen that the character of your senior players and the influential players and the drive within the team is critical.
“As the manager you are picking the team to represent you and in this instance your country and you have to have reliable people and you have to know what you are going to get.
“I often remember Terry [Venables] talking about a couple of players when he was England manager saying, ‘Well he’s a great player on his day but how do I know when his day is?’
“You are foolish if you ignore certain repeat signals that happen. Slightly long-winded answer, but the long and short of it is that I won’t judge people on what has happened now but for certain we build a picture of evidence.”