The 27-year-old, who made his second England start in Wednesday night's 2-1 win over Hungary, has been linked with a summer move to the Gunners, who are struggling for centre-backs following the departures of Sol Campbell, William Gallas and Mikael Silvestre.
A move to north London would be a step up for Jagielka given that Arsene Wenger can offer the defender Champions League football this season.
However Jagielka, who signed for the Toffees from npower Championship side Sheffield United in 2007, denies that he is seeking a move away from Goodison Park.
"There's nothing I can do about the speculation, but the gaffer has pulled me aside and told me I'm not going anywhere," Jagielka told talkSPORT.
"I'm happy with that. I'm an Everton player, I love playing for the club, and I'm just going to get on with my job there."
Jagielka marked his fourth England cap by unwittingly scoring the own-goal which put the Three Lions behind in their first match since their embarrassing World Cup exit to Germany.
The former Blades defender's embarrassment should have been avoided however, with replays showing the shot was cleared by Michael Dawson before all of the ball had crossed the line.
Jagielka was one of eight players not involved in South Africa who played Wednesday night's game, which England won courtesy of two superb goals from captain Steven Gerrard.
He now hopes to be part of a new era under Capello, who is determined to win a trophy with England before his contract runs out after Euro 2012.
"It did feel like a new era definitely," said Jagielka.
"If you looked at the team that finished the match then there won't have been many caps between us which is nice to see.
"We have a lot of good English talent coming up and I'm sure that the manager will put young and old together and hopefully we can kick on for the European Championships."
The Manchester-born defender said that the own goal will not overshadow his first international start at Wembley.
He said: "The goal was unlucky but overall it was a massive experience for me.
"It was the first time I've played at Wembley and the first time I've got some game time,"
"The lads did well to be out there and I was just as proud as punch to be out there."
Wednesday night's match was punctuated by booing from some home fans who directed their anger at the likes of Gerrard, Ashley Cole, Wayne Rooney and John Terry for their poor showing in South Africa.
Jagielka insists the players hold no grudges against those supporters and is confident that they will get behind the team when England begin their Euro 2012 qualifying campaign in September with games against Bulgaria and Switzerland.
Jagielka continued: "The fans pay their money to come and watch us and hopefully they'll keep coming to watch us.
"There's nothing that we can do about the World Cup now though.
"There are two important games coming up in September. We have to look forward. The European Championships will be a massive tournament for us and hopefully we can perform a bit better than we did at the World Cup."