Harte came through the ranks to make his professional debut at Elland Road and went on to make nearly 300 appearances for the club between 1996 and 2004.
The 34-year-old former Republic of Ireland international full-back agreed a further year at the Madjeski Stadium on Wednesday ahead of the Royals' return to the Premier League.
Harte told the Reading Post: "I got a phone call about 10 days ago saying they (Leeds) were interested.
"I love it down here and these have been the best two years of my career. It would be silly to leave such a fantastic club like Reading. I'm definitely happy where I am.
"I don't say you can never go back as I'm sure that would be fine. But people would say back in those days that we had a fantastic team, playing Champions League football, and it would have been difficult."