Few things are impossible, but...
The Mauser 98 action has a bolt face machined to accept cartridge cases of the size of 8x57, 30-'06, etc. The 223 Remington is obviously much smaller in diameter. That would pose a real problem that I doubt would be worth dealing with. You might consider the 22-250 as a 22 centerfire cartridge to chamber the 98 in. The 22-250 has the same size case head as the 8x57 and '06, and will work just fine.