Vardy, who retired from England duty following the World Cup in 2018, is the Premier League's top scorer this season with 19 goals, following his brace in Monday night's 4-0 win over Aston Villa.
With Tottenham Hotspur's Kane recovering from a hamstring operation he had in January and Manchester United's Rashford out with a back issue, Vardy has emerged as an option for the Euros in June and July.
"Who knows? Gareth and I both agreed the door would still be open for whatever reason and then we would sit down and have a talk about it [if needed]," Vardy, who has seven goals in 26 appearances for England, told Sky Sports.
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"We've not had the chat or anything yet and nothing has been spoken about. The lads [Kane and Rashford] are out injured, but they're looking to be back in time. So only time will tell."
Southgate said last week both Kane, who returned to training on Monday, and Rashford were on track in their recoveries but would not close the door on a recall for Vardy.
The striker admitted, however, that being out of the England side had helped him.
"I'm not going to lie, I've had a few extra days off in the international breaks so I've been able to switch off completely from football and it's always beneficial," Vardy said.
"Knowing that when you get back it's constant again, it's 100% football every day so it's one of those things that has benefited me."
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