A Saver Fare can be upgraded too, it just needs more cash. I think you may be looking at the options when upgrading using miles where a Saver cannot (until check in opens) but a Flex Fare can be done anytime.

An upgrade with cash can be done immediately, but as you've booked through a travel agent you may not be able to do it on the EK website. In addition, there will likely be agency fees to be added.