Everton boss David Moyes was open about the Gunners' approach, explaining the England international is still a crucial figure to his plans, and the 28-year-old insists that at no point did he feel unsettled.
A £4million buy from Sheffield United in 2007, Jagielka is eager to repay the club for the faith they showed after he was ruled out of the 2009 FA Cup Final through a cruciate ligament injury.
"It's different for me," Jagielka said in an interview with the Sunday Times. "I think it's just your type of personality. The gaffer here has been clever enough not to just buy players who suit us in footballing style, but he's bought the right characters.
"I'd like to think I'm grounded. I love playing football and I love being at Everton, and I'm not going to try to bully my way into getting a transfer.
"I've always felt loyalty. I found it really hard to leave Sheffield United. Here, I've been given a chance by a great club and hopefully playing here will lead to many more England appearances.
"Me and the gaffer spoke (about Arsenal) and he let me know where the land lay. I was more than happy with his explanation and I'd like to think the way I've played so far this season shows it's blatantly obvious that I'm happy to still be here.
"When I got my injury, Everton kept a promise to give me a new contract and you don't forget things like that. It's been a fantastic three years and the players and myself are excited about the possibility we can do something this year."
Jagielka returned from injury in February and although he was overlooked for the World Cup, he won his fourth cap and played his first full game for England in the recent friendly against Hungary.
He will be hoping to stay in the squad for the start of next month's Euro 2012 qualifiers but first his focus is on helping Everton kick-start their season after starting with one point from six.
The Toffees have been one of the biggest challengers to the 'Big Four' in recent seasons and Jagielka believes they can still compete despite big-spending Tottenham and Manchester City finishing above them last season.
"Top four is definitely possible and we have the belief that we can finish there but I think last season was when fourth was up for grabs and it's going to be harder now," Jagielka said.
"If you look at who's invested, what I'd say is we've not stood still but carried on walking where other teams have started to jog. Realistically, that's where we are.
"At the moment, it's maybe hard to have the same spirit as a year ago because it's such a big team and people are naturally disappointed if they're not playing," he added.
"I know it sounds strange but sometimes our strength has been backs against the wall, knowing we've only got 12-13 senior players fit for the next few months and now, every week, five or six internationals are missing out."