The controversial sales tactic was scrapped four years ago after 52% of customers were found to be paying higher bills after signing up to deals with cold-callers.
The Big Six energy provider said the competition watchdog should re-think its stance so it can help customers who do not shop around for deals online to find a cheaper tariff.
Its proposal has been put forward to the Competition and Markets Authority's Energy Market Investigation, which is reviewing ways of making it easier for customers to switch tariffs.
Rival energy company SSE is also calling for the ban to be lifted on face-to-face sales with customers.
Will Hodson, of consumer collective the Big Deal, said: "It's depressing but unsurprising that the Big Six are lobbying to bring back doorstep selling."
He added: "If the government is serious about cleaning up the energy market then they must not allow the return of Big Six doorstep selling."
Industry regulator Ofgem forced ScottishPower to pay customers £8.5m in 2013 following an investigation into its doorstep and telephone selling.
The energy company was found to have misled customers during sales approaches because its staff were not properly trained and monitored.
In its submission to the Energy Market Investigation, ScottishPower stated the CMA "should give more attention" to the negative impact the ban on "face-to-face marketing has had on customers (whether doorstep or otherwise)" who do not "use the internet or do not like to transact over it."
A spokesman for ScottishPower said it was "one of many ideas" it had submitted to the CMA to help customers switch to cheaper tariffs.
The CMA said it will publish a "provisional decision" on all recommendations by the energy suppliers in March, before concluding its investigation in June.
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