The 34-year-old departed the Hawthorns earlier this week, signing with Swedish club Djurgarden after nine years as an Albion player.
“It was close," Olsson told Expressen of a potential move to Tottenham in the summer of 2012. “Usually it's just rumours but this was pretty close to 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."