If your workforce comprises mostly of employees below the supervisory level (who can not give feed back on computers about their self perceived training needs), let their supervisors initiate the process by defining the collective needs of each team/ task force. And for Supervisors & above, let each one initiate their own training requirements.
Probably a good approach will be to provide to all Supervisors & above an inventory of programs 'on line' (with full details of the coverage of each program), & asking them to pick up the programs most relevant to their needs. To ensure that the choice of programs is capped by the total number of days an employee can be spared for training, indicate the duration of each program in the inventory. To further ensure that the TN I process is aligned to the organizational objectives, let these self-identified training needs be approved by the immediate reporting manager/ at an appropriate level in the organizational hierarchy.
A consolidation of the above inputs leads to the finalization of training calendar for the organization. This is followed by scheduling of programs, in such a manner that the work place availability of people is not jeopardized. This implies that nominating employees for participating in a specific capsule of a program (there may be six capsules of the same program during the year) is left to the discretion of the Manager to whom the employee directly reports.
To manage & track this complex activity, you need a training management system for an organization of your size. 'EmpXtrack' is an available solution preferred by many organizations. You may search for the same on the web & evaluate if it can support your needs.