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Southgate said the Leeds United striker was "very close" to being included in his squad for upcoming World Cup qualifiers, but he ultimately opted to give a first call-up to Aston Villa's Ollie Watkins.
The Three Lions boss also described Bamford as "very unfortunate" and added, "Patrick's a player we're very much looking at as well."
Bamford not being selected had led to some speculation suggesting that he could switch international allegiance to the Republic of Ireland.
Eligible to play for Ireland through a grandparent, Bamford was capped once at Under 18 level in 2010 before going on to represent England at Under 18's Under 19's and Under 21's.
In recent years both Martin O'Neill and Mick McCarthy tried to convince him to play for Ireland and current boss Stephen Kenny has been told that Bamford still dreams of playing for England, his birth country.
"He said that he wouldn't like to stand in the way of another Irishman," Kenny said, as per The Mirror.
"He said he wouldn't want to do that, that his desire is to play for England.
"I never actually got to speak to him because he said that his ambition was to play for England."
While Under 21's manager, Southgate called Bamford up to his Under-21 European Championships squad in 2015 but he had to pull out through injury.
Bamford has scored 14 goals in 29 appearances this season and after scoring the opener in Leeds' 2-1 win over Fulham on Friday, he said he remained hopeful of working his way into Southgate's plans.
"Every player who gets called up thoroughly deserves it. I think a few who thought they might get called up didn't and are disappointed," he told Sky Sports.
"I just need to keep working and see if I can get my name in contention for the Euros. If I keep going as I am I think I'm in with a shot. If you told me at the start of the season I'd be linked with England I'd say you were bonkers.
"If it comes, it comes. If not I'll know I've done my best. It was in the back of my mind a little bit I guess. It gives you a bit of an extra fire in your belly."
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