As indicated by Tim, in the first answer, no one can tell you if he will be qualified based on what you have told us.
However, I think your real questions are:
1. Can he use his retirement income to qualify for a loan? Absolutely.
2. Can he buy a new home before selling his current home? If he qualifies, Yes. The lender will want to be able to prove he is in the process of selling (current home listed on MLS, etc.) to consider the new home his primary, or they may just treat the new home as a second home. The lender will most likely include his current home's expenses in his debt ratio--real estate taxes, homeowners insurance premiums, HOA dues, if any, etc.
I hope this helps. Anything else?