No he shouldn't. If Conte had wanted to get rid of a couple of players last year and he's now gone would that have made sense?The manager should have the most important say on current players’ contracts being extended or not.
A manager's input should be "I want a player that has attributes x, y and z" and then the DoF tries to fulfil that. The manager shouldn't be doing anything with contracts.
If the manager's style doesn't fit in with what's in the squad then it's a failure from the DoF to get the right manager or the right players for the style.