Aidan Vaughan, managing director of MPL World Management spoke on Premier's News Hour after Britain's high street banks were told to get started on a technological "revolution" to help promote better competition within the industry.
The proposals also include a new duty on banks to introduce maximum charges for customers who used an unarranged overdraft.
The former-chairperson of Association of Christian Financial Advisors said: "If occasionally, we go overdrawn and don't realise it, I think that this idea of sending texts to alert you when you've gone over or are about to, is a very good idea."
The new plan comes after a two-year inquiry by the Competition and Markets Authority (CMA), which has said new phone-based apps should be brought in by early 2018.
The CMA has unveiled a package of measures to help customers to shop around to get a better deal, after finding older and larger banks do not have to compete hard enough for customers' business and newer and smaller banks find it difficult to grow.
Aidan Vaughan said changing bank is hassle at present.
He said: "Very few people look to change their banks, it would be a major financial change in their lives and for businesses it's very much that they like to keep the same bank because it looks good with the auditors."
It also wants a new app that could allow you to manage all your different accounts in one place.
This could mean, for example, that rather than having to constantly check their bank account themselves to avoid going in the red, someone could pre-instruct their app to move money from another provider into their account if they are about to go overdrawn.
Automatically moving money about in this way could help customers avoid unwittingly being hit with charges.
Aidan Vaughn added: "All of my three children do bank with a mobile phone, personally I don't, but I'm sure it's coming.
"And I think very shortly we'll all be doing our washing up on a mobile phone!"
Listen to Premier's Alex Williams speak to Aidan Vaughan here:
