Uncertainty shrouds the future of current incumbent Martin Johnson, following a highly disappointing World Cup during which the squad were criticised for their performances on the pitch and behaviour off it.
It is unknown whether Johnson wishes to continue as manager or if the Rugby Football Union want him to remain in charge.
However, Mallinder, a former England Saxons coach who won two England caps in 1997, would relish the challenge the job offers.
The former Sale full-back told several national newspapers: "Every player should want to aspire to play for his country and I think that's probably the same for coaches too. You should always aspire to be the very best you can.
"If one day, I ever have that honour, it would be something that would be very difficult to turn down."
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The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
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The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
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The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.
