I would not recommend this conversion. There are a couple of reasons:
Yes, theoretically you could ream the chamber to .300 Win Mag. This photo shows a .300 Win Mag reamer with a .308 Winchester cartridge. As you may be able to tell, the reamer will begin cutting way before the pilot engages the bore of the barrel. That means that the reamer will be unsupported. That could cause a chamber that is not concentric with the bore or which may be too large at the rear, etc.
.300 Reamer by
jakefromclemson, on Flickr
This photo shows a .300 Win Mag cartridge feeding into the throat of an unmodified Model 98 Mauser receiver. it hangs up with a couple of inches left to go. That is because you MUST open the feed rails to feed magnum cartridges so that the cartridge will feed up throught the bottom of the receiver. This is true whether you are using the original staggared box or an after-market single stack box. If the rifle is a controlled round feed action, the cartridge has to ride up under the extractor.
.300 FeedRails by
jakefromclemson, on Flickr
Bill Jacobs