Howe says it is not something he would be interested in, at least for now.
"I never say never, never say, 'No, it won't be something I am interested in'. But in the short term it is not on my radar at all. It is all Newcastle and trying to make this team better," said the 44-year-old.
"I have always said I love the day-to-day coaching, love being with the players on the training ground. International football you get that taken away for long periods.
"At this moment in my life, that is not something I want to do."
Howe, however, was also full of praise for Southgate, with whom he has a good relationship.
"Gareth (Southgate) has done an incredible job, and I mean that from the bottom of my heart," he said.
"I have been lucky enough to go in and see him work and I have a lot of time for him and Steve Holland. They have been amazing for England. You have to remember where England were before he took over and what he has done for the country."