The Ligue 1 champions spent big this summer on Angel Di Maria from Manchester United and reportedly tried to capture Ballon d'Or winner Ronaldo as well.
It is understood a £110million offer was made for the former Manchester United star - but Real Madrid rejected the offer.
The 29-year-old front man joined the Black Cats on loan from Rennes this summer.
He made his Sunderland debut as a half-time substitute in their 2-2 draw at Aston Villa last month.
And he told the Northern Echo that a switch to English football was offered to him earlier in his career.
“I have had opportunities to come to the Premier League before," he revealed.
"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.”
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That is according to the Daily Star, who claim Januzaj - on loan at Dortmund for the season - is not expected to return to Old Trafford.
The Bundesliga club value Reus at around £60m, with Manchester City thought to be keen on the 26-year-old before their swoop for Kevin De Bruyne this summer.