Two wins from two means that England are already assured of a place in the last 16 of the competition, which Southgate believes will make his decision on whether to risk Alli against Belgium later this week easier to make.
"Dele is progressing well," he told reporters. "He's had an opportunity to train on the field and we'll know exactly how close for the Belgium game after [Monday].
"It takes pressure out of the decision for playing in that game but if he's ready it's a good opportunity for him."
Alli took part in training on Monday morning with the rest of those who did not start against Panama.