The development comes after The Herald reported in October that chief executive Ignacio Galan regarded the sale of the stake as just "fifth or sixth priority".
He said then he would prefer to sell other less attractive assets and that the disposal of a stake in the ScottishPower business "might not be required".
Mr Galan regards the United Kingdom, alongside Spain and the United States, as a core market for the group. He has praised the consistency of UK power regulation.
The ScottishPower business in question owns and operates a network of cables and power lines that transport electricity to around 3.5 million homes in Scotland, northern England and Wales.
The Herald understands that the touted sale, which could have netted Iberdrola £1 billion, has been shelved after the group made good progress selling other businesses.
It would have seen Iberdrola sell a 49% stake in the ScottishPower business.
In the first nine months of last year the networks business produced earnings before interest, taxation, depreciation and amortisation of €676 million (£562m). This was up 14% on the same period of 2011.
It is attractive to investors because the highly regulated business produces stable and predictable revenues.
It had attracted interest from major international investors understood to include the Ontario Teachers' Pension Plan, Canada Pension Plan, Borealis Infrastructure and Australia's Industry Funds Management.
Iberdrola is seeking to offload €2bn of assets.
It is part of a drive by Mr Galan to slash its debt by €6bn to €26bn by 2014 and preserve its investment grade credit rating, even as Spain's sovereign rating remains under pressure.
The power utility disposed of a greater than expected €850m of non-core assets last year.
This included a portfolio of 32 wind farms in France which was sold for €400m.
It sold stakes in American companies Energetix and NYSEG Solutions to Direct Energy, owned by Scottish Gas's parent Centrica, for $110m.
A stake in Gas Natural Mexico went to a subsidiary of Japan's Mitsui for $82m.
It is also thought to be about to sign a deal to sell wind farms in Poland.
But it is understood that Iberdrola might yet dust down the plans for the ScottishPower stake sale at a latter date if necessary.
Last year Iberdrola raised £350m through an over-subscribed offering of bonds by the Manweb distribution subsidiary of ScottishPower, which operates in Wales and England.
There have been no plans to sell any part of the company's retail or renewable energy divisions.
A ScottishPower spokesman said: "We do not comment on speculation."
In October Iberdrola revealed plans to slash investment to €3.5bn per year for 2012/14, meaning a reduction in more than one-third from the 2009/11 period. But the UK will get around €4.4bn over the three-year period. Much of this will be ploughed into large projects such as upgrading the electricity interconnector between Scotland and England and building a subsea link.
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