Magpies boss Benitez has been named as one of four managers who could pick up the prize for October, with his side having won all five of their league fixtures - against Rotherham United, Brentford, Barnsley, Ipswich Town and Preston North End - last month.
The other three managers on the shortlist are Preston's Simon Grayson, Leeds United's Garry Monk and ex-United boss Chris Hughton, now in charge at Brighton & Hove Albion.
Forward Gayle, meanwhile, is also in with a shout of picking up an award as Player of the Month.
The former Crystal Palace frontman bagged braces against Brentford and Barnsley in October, racking up four goals from his four games to take his tally for the season to 11.
He is up against fellow nominees Sone Aluko of Fulham, Brighton's Lewis Dunk and Reading goalkeeper Ali Al-Habsi.
The winner will be announced on Friday.