The Sweden international is said to be interesting Bournemouth, as he looks like leaving Roazhon Park before the new season.
The Sweden international moved to France last January for £2 million say the Echo, after spending a large part of his career in the Netherlands, but Toivonen has found himself out of favour at Rennes this summer, and the 29-year-old is available for transfer.
Rennes manager Philippe Montanier told the French press that there had not yet been any contact from Sunderland for the player, saying: “We have not received any offer”, when asked about the Black Cats's interest.
Toivonen played 35 times last season for the Red and Blacks, scoring on seven occasions as the Brittany side finished in ninth place in the French top flight.
But he is most famous for spending four and a half years at PSV, where he scored 61 goals in 139 league games.
Dick Advocaat was the Swede's manager for one of those season, helping the Dutch giants to second place in 2012-13. Toivonen missed a chunk of that season with a torn hamstring, but still managed to score 10 goals in 24 games. The Echo reported on speculation Sunderland were considering signing the player, with his ability to play both as an attacking midfielder and a forward something that would cater to an area the Black Cats are looking to strengthen in.
Time will tell if Toivonen's old boss will firm up interest in the former Malmo man, having already recruited one former PSV star this summer in Jeremain Lens.