The Sky Blues boss described the Dutchman as "one of the best strikers in Europe" and named him as a summer transfer target, The Mirror reports.
However, the Italian went on to say that he expects van Persie to remain with the Gunners despite his efforts to persuade him otherwise.
"We are interested in all good players," said Mancini. "This is normal, but not only us. I think all the good teams are interested in Van Persie.
"I think Van Persie at this moment is one of the best strikers in Europe with Messi, Ronaldo and with Sergio and Mario. I think he is a fantastic striker, but I think he will remain with Arsenal."