He made his debut in Sunderland's 2-2 draw at Aston Villa before the international break.
But the 29-year-old revealed to the Northern Echo that he was offered the chance to join Liverpool in 2010 under then-manager Roy Hodgson.
“I have had opportunities to come to the Premier League before," the Sweden international said.
"A couple of years ago it looked like I would be joining Liverpool when Roy Hodgson was there. Not fighting hard enough for that to happen is something I regret in my life.
“I am 29 so when I look back I will be pleased that I took the opportunity to move to France to try out a new league also.
"I experienced how it is to live there, experienced a new language and culture so it was a nice time.
"But I always wanted to play in the Premier League so when I got the call from Sunderland it was a quick decision to make.”
Newspaper Review - Monday 7 September
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The Echo also claim Newcastle were another team interested in Toivonen back in 2010 - but that Advocaat blocked the move away from PSV.
Sunderland have got off to a rocky start in the Premier League this season - recording two draws and two defeats.
They face Tottenham at home this Sunday (1.30pm) before a trip to Bournemouth a eek later.