According to Tiefenbacher,
Egg white is naturally alkaline with an initial pH of 7.6–7.9 but in storage the loss of carbon dioxide by diffusion through the shell increases the pH of the egg white up to about 9.7 with age.
The loss of $\ce{CO2}$ means loss of $\ce{H2CO3}$, an acid with pKa of 6.3. This reduces acid and in a neutral solution pH would approach 7. Since it goes up towards 9-10, what is the base? Albumin is a buffer in biological systems but I don't think it is that strong a base. What is the alkali causing pH of around 9-10?