The 27-year-old former Arsenal player, a Seville native, told As sports daily on Sunday he had decided to leave even though Simeone was counting on him and added that his father's health had been a factor in his decision to seek a move.
"Sevilla are giving me the chance to return home," Reyes said.
"It's an option I have on the table which might never come along again and I want to make the most of it.
"They operated on my father a few weeks ago and the best thing for everyone is to go back.
"I always wanted to return to Sevilla, it's an exciting goal for me to return to the team that gave me the chance to become a professional."
Local media have reported that Sevilla will pay Atletico 3.5 million euros to take Reyes back.
He left the Andalusian club for Arsenal in 2004 for a fee of some 17 million pounds, a club record for the English Premier League side at the time.
However, he struggled to adapt to life away from home and was loaned to Real Madrid two years later before signing for Atletico in 2007.
He has clashed with several coaches, most recently Atletico's Gregorio Manzano, who was sacked last month and replaced by former Argentina captain Simeone.
Reyes made 21 appearances for Spain, scoring four goals, and last played for the world and European champions in August 2006.
