The Reds have held a long-term interest in Toivonen having made enquiries for the Swede during the summer transfer window.
It has been suggested they could make a new move for the 24-year-old to add to their attacking options when the transfer window reopens in the New Year, but Toivonen expects to stay in Holland.
"I know that there are clubs looking at every game so rumours are something that I have to live with."
Asked if he felt a move away from PSV in the summer was more likely, Toivonen said: "I don't know. The most important is that I get to play every game like I do now and play in a team that has the chance to win the league.
"It would be fun to get a gold with PSV. We have a perfect harmony in the club."