Jones features on a shortlist of four alongside Leicester rugby director Richard Cockerill, Saracens' Mark McCall and Wasps' Dai Young, Premiership Rugby has announced.
The winner will be revealed at the Premiership awards dinner in London on May 9.
London Welsh finished bottom of the Premiership this term and now face a return to the Championship after just one season of top-flight rugby.
But Jones won many admirers for producing a competitive squad that won four games, including victories over Exeter and Bath.
Welsh also faced the considerable obstacles of their Premiership status not being confirmed until late June last year, and then having five league points deducted for fielding an ineligible player.
Cockerill and McCall, meanwhile, have both guided their clubs into the Premiership play-offs, while Young oversaw a Wasps revival following last year's relegation-threatened campaign.
Wasps were on the verge of a play-off place at one stage this season, although they are currently in eighth place, while they also reached the Amlin Challenge Cup quarter-finals.