The Rolling Stones star and the Pulp frontman are both up for the Best Music Programme honour for their popular shows on the British airwaves. Wood has a weekly programme on the Absolute Classic Rock radio station, and Cocker fronts a series for Bbc 6 Music.
They will compete against professional broadcasters Zane Lowe, Dermot O'Leary and Lauren Laverne for the trophy.
Wood picked up the Music Radio Personality of the Year prize at the Sony Radio awards in 2011, and Cocker picked up the Rising Star honour the year before (10).
After hearing of his nomination, Wood wrote in a post on Twitter.com, "Thank you Sony Radio Awards... The Ronnie Wood Show/Absolute Radio has just been nominated for Best Music Programme. Great news!"
Former Catatonia singer Cerys Matthews is also in competition against jazz star Jamie Cullum for the Music Radio Broadcaster of the Year award for their Bbc radio shows.