Everton's Pickford played in Friday's 1-0 win over the Netherlands and impressed with his distribution, an important attribute for Southgate, who wants the team to play out from the back and control possession.
"I thought Jordan played really well last Friday... and it's motivation for us all," Butland told reporters.
"It's a great way to go into a World Cup. Whoever is selected will be coming in off a battle, which is what you want. It's probably a four or five horse race still."
Though Southgate is likely to field a much-changed side against the Italians, he will not deviate from his preferred three-at-the-back formation, with John Stones expected to keep his place in central defence.
Stones has found playing time hard to come by for Manchester City of late, but is key to the way England are trying to play under Southgate, given his ability to pick a pass and comfort on the ball.
The 23-year-old has been frozen out of the City team by a combination of January signing Aymeric Laporte, the vastly improved Nicolas Otamendi and the return to fitness of skipper Vincent Kompany.
"It's difficult," Stones said of his lack of game time at club level. "Every player wants to play week-in, week-out, but I've had games here and there.
"I felt sharp and back to myself (against the Dutch) and I want to build on that for Tuesday. We created a lot of chances from playing out (from the back) and that's a massive thing.
"Everyone's on board with it. If the odd mistake is made, you've got to stay mentally strong and not shy away from it."
England open their World Cup campaign against Tunisia in Volgograd on June 18, before matches against their other Group G rivals Panama and Belgium.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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