最简单的方法是使用一个类型参数，将函数的参数类型表示为元组：

class Process<T extends any[]> {
  readonly fn: (...args: T) => any;
  readonly parameters: T; // doing sth here to have the types inferred based on `fn` args
  
  constructor(fn: (...args: T) => any, parameters: T){
    this.fn = fn;
    this.parameters = parameters;
  }
}

function doTask(task: string){
  console.log(`doing ${task}`);
}
const message = new Process(doTask, ["Something"]);

Playground链接

为此，您可以使用类型参数：

class Process<F extends Function> {
  readonly fn: F;
  readonly parameters: any | any[]; // doing sth here to have the types inferred based on `fn` args
  nextMessage: Message | null;

  constructor(fn: F, parameters: Parameters<F["apply"]>) {
    this.fn = fn;
    this.parameters = parameters;
  }
}

它所做的正是您所期望的，提取参数类型。
它是这样实现的：

/**
 * Obtain the parameters of a function type in a tuple
 */
type Parameters<T extends (...args: any) => any> = T extends (...args: infer P) => any ? P : never;