According to Chilean sports daily Triunfo, the 24-year-old Vidal, who scored the winning goal for his country in their 2-1 victory over Mexico at the Copa America on Monday, is being chased by the Serie A side.
He would be paid an annual salary of 3.7 million euros (5.3m US dollars), if the deal goes through.
Bayern are reported to have offered 10 million euros for Vidal, way under Bayer's asking price of around 15 million euros, with the attacking midfielder under contract until June 2012.
And Serie A team AC Milan are also reported to have matched Bayern's bid for Vidal.
"Arturo is a sought-after player, there are several requests for him," Bayer Leverkusen's director of sport Rudi Voller said at the Bundesliga team's pre-season training camp in Austria.
"His winning goal for Chile means that he is not cheap.
"He will only switch to a foreign club when the price is right.
"In any case, we are sticking to our original plan and we see him staying with us."
For the meantime, Voller ruled out Vidal joining another Bundesliga club.