Hussain quit as skipper of the one-day side after England's elimination from the World Cup, citing the increased pressures of the job as one of his reasons.
But the 34-year-old said he wanted to continue as captain of the Test team.
Speaking in his column in the Sunday Telegraph newspaper, Hussain said he believed splitting the captaincy on a permanent basis will make both jobs easier.
"On tour you have so many questions about so many things apart from yourself and England's cricket," said Hussain.
"You have to talk about injuries, opposing players, about the International Cricket Council, the ECB, about political issues like Zimbabwe.
"Splitting the captaincy would help me if I was asked to stay on as Test captain and it would also help the new one-day skipper settle into the job.
"If the whole captaincy is landed on one new individual, something in him will have to give."
Australia are already experimenting with separate international captains, with Ricky Ponting as one-day skipper and Steve Waugh leading the Test side.
Batsman Michael Vaughan said England's players wanted Hussain to carry on as Test captain.
"We'll be delighted to play under Nasser for a bit longer," said Vaughan, who is one of the leading candidates to replace Hussain as one-day captain.
"He's done a good job with the Test team. His batting was very good in the winter against Australia."
Hussain endured a difficult tour of Australia before being heavily involved in the lengthy negotiations over England's boycott of the World Cup game in Zimbabwe.
"All the time we were in Australia we were looking forward to the World Cup, and now none of us will look back on it fondly," Hussain said.
"I would like to go back to doing what I wanted to do as a boy: to play test cricket for England, not be a national spokesman for everything cricketing."
England face two tests against Zimbabwe in May and June, followed by a one-day series and a five-match test series against South Africa starting in July.