According to Blindside sources, the former England hooker is torn about taking the job as the fallout for Alex Codling's departure from Jones' staff rocks the RFU.
Codling joins a long line of coaches to leave the RFU in the Jones era after it was alleged he had a disagreement with the tough Australian task master following a presentation.
Cockerill is keen on moving into the international game after working at club level for Leicester Tigers, Toulon and Edinburgh.
He sees Test rugby as a natural career progression and he would be in pole position if Jones quits after the next World Cup.
BY NEIL FISSLER