The bloc's securities regulator ESMA surprised the sector when it wrote to the European Commission to say stricter conditions may be needed for delegation, or when asset managers outside the bloc pick stocks for funds domiciled in major EU fund centres like Luxembourg and Dublin.
Delegation has become politically sensitive due to Britain, where many asset managers pick stocks for EU funds, leaving the bloc in January.
ESMA suggested "clear quantitative criteria" on the number of senior officials a fund must have where it is domiciled.
"What we have not seen in this letter from ESMA is much of an explanation, much of the evidence that actually would explain why a change from the current arrangements is actually necessary," said Michael Collins, director of government affairs at M&G.
"The case has not yet been made," Collins told an online conference held by Luxembourg funds industry body Alfi.
Sheila Nicoll, head of public policy at Schroders, said regulators were still wedded to the idea that physical and geographical presence mattered when it came to supervising funds.
"It seems to me that actually COVID-19 has shown us that that doesn't matter," Nicoll, a former UK regulator, said, referring to an industry where many have worked from home since pandemic lockdowns began in March.
"I can be subject to Italian rules or French rules or German rules or Luxembourg rules whether I'm sitting in London or I'm sitting in Amsterdam or Milan. The crisis may cause us to think a bit differently about this," Nicholl said.
Martin Parkes, managing director of public policy at BlackRock, said it was important to bear in mind the value of delegation in allowing investors to access the widest range of investment opportunities.
By Huw Jones and Carolyn Cohn