The 21-year-old midfielder is gradually becoming a key man in Foxes boss Brendan Rodgers' plans since returning to the club from a loan spell with Championship side West Brom in January.
Barnes scored nine goals in 25 league appearances for the Baggies and then added a further goal in 16 Premier League appearances with Leicester in the second half of last season.
He penned a new five-year deal in the summer and has made two substitute outings in the opening three games this term, scoring a stunning goal in last weekend's 2-1 win at Sheffield United.
Barnes helped England Under-18s win the Toulon Tournament in 2017, has 10 caps at Under-20 level and is now a regular in the Under-21s.
There has been talk of Barnes emulating team-mate James Maddison and securing a call-up to Gareth Southgate's senior squad, especially after the Three Lions boss witnessed his goal at Bramall Lane.
However, the youngster is just happy to focus on club matters and trying to become a regular starter for the time being.
"For me at the minute, it's about club football," he said. "I need to secure my place in the team. That's not something that's on my mind at the minute.
"It's just about cementing my place in the team at Leicester, and making sure my performances and my stats are up there. It's too early for me.
"You're not going to get called up to the England team unless you're playing for your club."