Edwards was briefly a free agent after the World Cup but revealed, after agreeing a new four-year contract with Wales, that there had been no contact from Twickenham.
Edwards' new deal with Wales allows him to spend one day a week working with an Aviva Premiership club and he has been linked with a role alongside Cockerill at Leicester.
The Rugby Football Union were criticised for not approaching Edwards, who won eight trophies during a decade at Wasps and helped Wales reach the World Cup semi-finals.
The RFU, who are currently undertaking a review of England's disappointing campaign in New Zealand, are still in a state of upheaval.
They are without a permanent chief executive, they are yet to appoint a permanent Professional Rugby Director - Rob Andrew is filling the role in a caretaker capacity - and Martin Johnson's future as England manager is still undecided.
With all that occupying the senior management at Twickenham, Cockerill was not surprised no-one made contact with Edwards.
"You'll have to speak to Rob Andrew. I don't know who is making those decisions," Cockerill said.
"I suppose they need to decide who is coaching the side first before they start recruiting staff."
Johnson is out of contract at the end of December while the future of his coaching staff - Graham Rowntree, Mike Ford, John Wells and Brian Smith - is also up in the air.
Meanwhile, Cockerill said that Leicester have not held any negotiations with Edwards but he is not against bringing in some external expertise.
Cockerill and assistant coach Matt O'Connor currently run Leicester's defence.
"We are looking at things all the time," Cockerill said.
"We have not defended as well as we would have liked and we are looking at that all the time.
"If we feel it right to bring someone in to help us with that, I am not against it. I have no interest in who makes us better, I just want us to be better.
"We have a very good environment, a very settled environment and you always want to be conscious who you let into that environment. That is nothing to do with Shaun Edwards, that could be anybody.
"At the moment we have had no discussions."