The 26-year-old midfielder now faces a race against time to prove his fitness to Southgate, who will be monitoring players that are in contention during the remaining games of the Premier League campaign.
"I don't think it's too late for anybody," Southgate told reporters.
"It is obviously more difficult because there are a couple of guys who have been in squads and not had the chance to play for us.
"We will still be monitoring everybody between now and the end of the season because there is probably a squad of 31, 32 players that are in contention and none of us know what is going to happen in the next eight to 10 weeks."
Southgate will also be without talismanic goalscorer Harry Kane against Italy on Tuesday as he continues to recover from an ankle injury.
"I don't know when he'll (Kane) be back, but he was confident that would be sooner rather than later," Southgate added.
"His mindset is very positive. None of these lads wants to miss games."
England have three more warm-up games before the World Cup in Russia, having beaten the Netherlands 1-0 last week.
Forward Raheem Sterling has urged the home supporters to show the team some love in the buildup to the World Cup as they prepare to face the Italians at Wembley.
Southgate's side have gone five matches without conceding a goal but have failed to produce much fluid attacking football themselves and scored just three times in that period.
"I feel sometimes there is too much negativity," Sterling told BBC.
"If you want your country to do well, as everyone says, bring a positive light into it. Make the boys go off to the World Cup with clear heads, knowing everyone's behind them, everyone's with them."
England begin their World Cup campaign against Tunisia in Volgograd, Russia on June 18.
(Reporting by Hardik Vyas in Bengaluru, editing by Nick Mulvenney)
