Generally speaking, anything related to a reservation falls under the responsibility of the Reservations Manager, not the Front Desk Manager. This is true up until the day of arrival (or sometimes a day or two prior if the hotel pre-blocks rooms at that point).

That said, an extended-stay hotel might not have a full on-site Reservations Office. Additionally, the person that handles these types of requests may have a different title besides Reservations Manager. For example, it could be the Sales Manager.

My advice would be to call the hotel during normal business hours. Tell the person who answers that you want to speak to someone at the hotel about upgrading your existing reservation. Be sure to emphasize "at the hotel" so you don't get transferred to Marriott Central Reservations. This request is fairly common, so the operator should know which staff member can help.