In its consultation the Law Commission also asks the public what the main barriers they see to people making a will and to tell it about their own experiences of disputes over wills following the death of a loved one. The paper also asks whether the rule that marriage revokes a will should be retained or abolished.
Commenting on the announcement, James Antoniou, head of wills for the Co-op, warned about any watering down of current rules.
"Making the law more accessible is one of today's biggest challenges facing the legal industry.
"However, at the moment, the laws about what makes a will legally valid are strict and clear.
"So any relaxation of these rules, by giving the courts power to recognise other types of communication, creates uncertainty which could lead to a greater number of legal disputes and ultimately with families suffering the associated legal costs."
The Co-op has been championing the need to make will writing more accessible by launching their online will service last year to the general public.
This allows people to start making their will online 24 hours a day, 7 days a week and then have a follow-up telephone call with a wills specialist to discuss their circumstances before it is put in place.
Once the will has been signed, Co-op can check the will to ensure that it has been executed correctly and also offers free lifetime storage.
Fiona Tait, technical director, Intelligent Pensions welcomed the Law Commissions proposals.
"It should be possible in this day and age for people to make their wishes clear in a way that is legally valid and not too onerous.
"Electronic wills would certainly improve existing access and make it easier for people not only to set up a will in the first place but to ensure it kept up to date as circumstances change.
"People are living longer and it is increasingly likely that they will have to make more than one will over the course of their lives."
Alan Lakey, director Highclere Financial Services, also backed the plans.
"These are important improvements which will assist in moving will making from the musty old world of quill pens into the modern age. Too many people leave their affairs in disarray to the advantage of others including HMRC."
Malcolm McLean, senior consultant at Barnett Waddingham, the industry needs to encourage people to make a will, "and not put them off by undue formalities and rigid rules".
However he added: "I'm not sure about voicemail and texts though. That may be going too far and could be risky."