Previously, Bayern were interested in signing Vlahovic from Juventus. however, because of the price offered by Juventus and Bayern's proposal which was rejected. in the end, Bayern again targeted Kane as their main priority. it would be very natural, if Tuchel wants a striker who is very ready to compete in any league. that's why, Tuchel insisted on bringing Kane to Bavaria.
Bayern Munich most probably expected a way lower asking price compared to Kane's. But as far as I know Juventus don't want to accept any bid below his current market value - 70 million euros. In this situation they must have preferred to bring Kane instead. In the end he is way more experienced and one of the numbered strikers in the world also.
Juventus might not even be able to sell Vlahovic according to the things going on recently. Because PSG are said to have an interest in Hojlund also. Bayern Munich's situation is like we discussed. Maybe Real Madrid might be interested in Vlahovic for this season but I don't know.