Jones set to lose one of his coaches
Harlequins finished a lowly 10th in the 12-team Premiership this season, with their now former Director of Rugby John Kingston announcing in April he would leave at the end of the campaign.
Gustard has been England's defence coach since January 2016 and was one of the first appointments made by Australian head coach Eddie Jones when he took over after the team's first-round exit at the 2015 World Cup.
The former Saracens flank is under contract with England's governing Rugby Football Union until after next year's World Cup in Japan, with Gustard currently in line to take his place among Jones's staff for next month's three-Test tour of South Africa.
He helped former Wallaby and Japan boss Jones guide England to two Six Nations titles in his first two seasons in charge only for the side to suffer a slump this term as they finished fifth.
Last week saw Jones label suggestions that Gustard might be making the short journey from England's headquarters at Twickenham to Harlequins's Twickenham Stoop ground in southwest London as "rumours".
"I don't have a contingency plan for staff, I don't have one for every staff member," Jones added. "If a situation arises then I'll deal with it."
Agence France-Presse
