He could try to appoint him, but unless Reid is able to pass his filibuster reforms, I don't see how he could get Senate confirmation.
Reid may want to reconsider his reform idea, too. The Republicans were calling for that years back, when they had a majority in the Senate. I pointed out to my dad, who was all for that idea, that he might not like the results when the pendulum swung the other way.
And the pendulum eventually always does swing the other way.