The 34-year-old departed the Hawthorns earlier this week, signing with Swedish club Djurgarden after nine years as an Albion player.
However Olsson could have left West Brom much earlier as he revealed that Redknapp twice tried to sign him between 2012 and 2015.
“It was close,” Olsson told Swedish publication Expressen of a potential move to White Hart Lane in the summer of 2012. “Usually it’s just rumours but this was pretty close to be being done.
“Then Harry was fired and they brought in Andre Villas-Boas, so it never happened.”
Of later interest from QPR Olsson added: “It was not as close. I had a good season with West Bromwich and QPR then tried to line up a deal. Harry Redknapp liked me.”
Olsson would go on to make 262 appearances for West Brom but the two parties agreed to terminate the defender’s contract early so he could return to his homeland.