Former England striker Alan Shearer, now a TV pundit, has led calls for the pair to replace Harry Kane and Raheem Sterling, neither of whom made much impression in the opening 1-1 draw with Russia nor in the first half against Wales.
Kane, the Premier League’s top scorer, had barely touched the ball in the opponents’ penalty area in either game.
Yet it took Vardy just 11 minutes to fire the home the goal that put England back on level terms, while Sturridge found a way through a crowded penalty area to snatch the winner in stoppage time.
Of the possibility of starting, Vardy says: “Yeah, I’d be more than happy with that.
“It’s down to me on the training field to put the extra work in and hopefully dislodge one of the players if I can do.”
A win against Slovakia would seal victory in Group B and see England paired with one of the third-placed teams in the round of 16, giving them an excellent chance of advancing further.
Their biggest threat is likely to come from Slovakia’s attacking midfielder Marek Hamsik, who laid on one goal for Vladimir Weiss and scored the other with a curling shot in his team’s 2-1 win against Russia.
Weiss tipped Sturridge, his former teammate at Manchester City’s academy, as a danger man for England.
He says: “He is an extraordinary player, which can be seen both on the club and national level.
“On the other hand, all their players are quality. It is necessary to be ready for them all.”