Farrell's decision to remain with Saracens has left a vacancy for a specialist backs coach in Stuart Lancaster's England management set-up.
RFU chief executive Ian Ritchie vowed to deliver Lancaster a "world class coaching team" to take England into the 2015 Rugby World Cup.
Smith, the attack specialist who was part of New Zealand's World Cup-winning coaching team, is widely considered to be the best in the global game.
If Lancaster wanted Smith then the RFU, having failed to persuade Farrell to sign up, would have to convince the former Northampton director of rugby to leave New Zealand and his current role coaching the Waikato Chiefs.
Smith confirmed there had been no contact with the RFU and said: "I'm really happy here at the moment. I'm close to family and enjoying the game.
"The NZRU have been great to me and I'm not desperate to coach overseas although one day I'd like to be in the Test arena again."
Smith's position appears to have shifted since he revealed in March he would be interested in a role with England, once the RFU had decided on who would be the new head coach.
Lancaster had wanted to retain the same interim coaching team that guided England to second place in the RBS 6 Nations, which meant recruiting Farrell from Saracens on a permanent basis.
After two weeks of negotiations, Farrell announced on Thursday he had decided to remain with the Aviva Premiership champions, amid reports that the talks had stalled.
Harlequins' former All Blacks fly-half Nick Evans tweeted: "The RFU need to sign up Wayne Smith... it's a no-brainer!!!"
Unless circumstances change, Smith would not be available for England's summer tour of South Africa due to his commitments with the Chiefs.
That would mean the RFU having to appoint another interim backs coach for the three-Test tour, with Mike Catt from London Irish and Clermont Auvergne's Alex King are both potential candidates.
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