Political tensions between England and Russia have developed following the attempted murder of Russian former spy Sergei Skripal and his daughter, Yulia, by use of a nerve agent in Salisbury.
Prime minister Theresa May confirmed all UK politicians and members of the royal family will boycott the event in protest, while foreign secretary Boris Johnson has compared the World Cup being hosted in Vladimir Putin's Russia to the 1936 Olympics in Nazi Germany.
"It's little interest to me what the foreign secretary thinks about it," Southgate told reporters ahead of Friday's friendly against Netherlands.
"I was in Russia last year for the Confederations Cup and there were about 15,000 fans from Chile, an incredible atmosphere in the stadiums. It felt like the other World Cups I'd been to.
"It means I have to answer different questions but there has been no suggestion we won't go to the tournament. The things that are uppermost in our minds are security and safety - and we have no concerns about that.
"Personally I would [go to the World Cup], I have spent some time in Russia and felt incredibly comfortable there.
"But for every individual it is up to them what they want to do, the situation is developing so we don't know what it will be like in June, but on the situation currently, it wouldn't stop me from going."