The Dutch club's sporting director Marcel Brands is not worried by interest in the Swede and thinks he will not move on during the current transfer window.
"I also read about that (Dalglish's trip) in the newspaper, but I didn't see him at the stadium and it is not important. We don't want to lose Ola during this transfer window, " Brands told fotbollskanalen.se.
"They called us last Thursday, in the morning, and asked how much we wanted for Ola Toivanen, but our answer was clear: we will not sell him at this point. We have not heard from them since.
"To have people from other clubs in the stands is quite normal. PSV are a big club and we get visits like that every week."