Rodgers, who signed Ings on a free transfer from Burnley in the summer of 2015 during his time as Liverpool boss, watched the 27-year-old sink the Foxes at the King Power Stadium on Saturday with an 81st-minute winner in a 2-1 victory.
The vital goal in the come-from-behind win took Ings' tally to 16 this season, with 10 of those in his last 11 Premier League games.
After ruling out a U-turn on international retirement from Foxes star Jamie Vardy in the build-up to the game, after it, Rodgers felt Ings is showing the form to add to the one England cap he collected in October 2015, and can fill the void vacated by Harry Kane who is out until April following hamstring surgery.
Asked whether Ings could step in for England, Rodgers replied: "Yeah, there's no doubt.
"When he was at his best in and around Liverpool he was certainly a player for that there. I would definitely say he would be in consideration for that.
"Danny has always been an outstanding player. He has an eye for goal, wants to run in behind. His goal was (typical) Danny Ings, really. Off the shoulder, in behind and he finishes it really well.
"He just needs to keep the consistency and availability and he'll show he's one of the best strikers about."
Southampton midfielder James Ward-Prowse echoed Rodgers' sentiments.
He said: "I think he should be in the next England squad.
"He's done more than enough already, not just for his goals, but the way he is working without the ball as well. He sets the tone for us with his pressing, along with Longy (Shane Long) up front."
Suggested to Ward-Prowse there was no better striker in the country at present, Ward-Prowse replied: "Probably not, no.
"It's great to see him doing well because he deserves it. Everyone sees the goals, but you watch us as a team and he sets off the press with Longy. He's getting his rewards."
Southampton's win was their fourth from their last five league games, lifting them up to 12th, just six points behind fifth-placed Manchester United.
Just two months ago manager Ralph Hasenhuttl seemed destined for the sack after a run of six defeats in seven matches, that included a 9-0 humiliation at home to Leicester.
Ward-Prowse, one of the six players who figured in that thrashing and who played on Saturday, has revealed Hasenhuttl showed the players "a motivational video of what happened before and what we've done differently until now" in the dressing room before kick-off.
"The fixture for us was a big one, considering what happened last time," said Ward-Prowse.
"That for us was the lowest point of our careers, and certainly for the club, so to overturn that with a win was massive. It proves that night was a massive wake-up call for all of us.
"We're a totally different side now and heading in the right direction. We showed that everyone is fighting and on the same page."