Ashton, who coached England to the final of the 2007 World Cup, is regarded as one of the world's premier attack coaches and along with New Zealander Wayne Smith had been linked with a role on Lancaster's staff.
Smith has turned down an approach from England for family reasons and Saracens coach Andy Farrell, who filled the role on a temporary basis during this year's RBS 6 Nations, has opted to remain with his club rather than join the national set-up full-time.
Mike Catt has been handed the role of attack coach for this summer's tour of South Africa after ending his association with London Irish, but it remains to be seen whether he will stay on beyond that.
Ashton has also been linked with the full-time post but told The Guardian: "There is nothing in the pipeline with England at the moment and it is a non-story. I always felt that Mike Catt was innovative as a player and if he takes that perspective and mentality into his coaching, he would be a real bonus to anyone.
"I think England have been looking for a coach who can help them find an extra gear in attack and I am sure that is what Stuart Lancaster will want Mike to do in South Africa. I hope that England will look towards the style of rugby that London Irish have played going forward under Catt as it's a very challenging game to defend against.
"He has to make sure though that all the basics are in place first, so that'll be the initial job. Once that's there then they can start to look to play in a slightly different way."
Ashton this week left his role as a consultant at National Division One club Fylde, with the Lancashire side saying he had "other options of work to consider".