Burnley's new sporting director Frank McParland hopes to be able to start next season alongside Sean Dyche.
Leeds teenager Alex Purver has agreed a new one-year deal with the club.
The Spain international could have reportedly increased his salary had he accepted a move to the Emirates Stadium.
"It is true that I had an offer from Arsenal that any player would have liked to have accepted," Juanfran said to marca.com.
"But I am very happy here.
"For me, as everyone knows, there is no better club than Atletico."
The 28-year-old joined the Colchonero club in January 2011 from Osasuna and has four years left on his contract at the Vicente Calderon.
Juanfran has been a regular in Diego Simeone's team and won the Europa League and the European Supercup with Atletico in 2012 as well as the Copa del Rey last season.