The Norwegian, 23, moved to the Etihad from Borussia Dortmund for £51m in 2002 and still has four years remaining on his deal.
However, the Daily Mail claims that Champions League holders City have “an appetite to lengthen that by at least another season”.
Discussions on increasing his current £400,000-a-week wages will be a “major blow” to Real Madrid.
They have a “desire” to bring Haaland to LaLiga and still have a “firm interest” in luring Paris Saint-Germain’s Kylian Mbappe to the Bernabeu after missing out on both over the past 18 months.
Haaland, whose father Alf-Inge also played for the Cityzens, went on to score a record-breaking 52 goals in his debut season at the Etihad as he fired Pep Guardiola’s side to the Treble.
Now City are “wanting to reward those exploits” with his manager “believing he can still improve”.
This fresh update claims that a “potential release clause” will be one of the main talking points in the new package.
Haaland initially had two inserted into his deal upon joining last year – with one dependent on Guardiola’s future prior to the Spaniard penning his extension in November.
The hotshot has already scored eight in ten matches this term.
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However, he drew a blank in Wednesday’s 3-1 win at RB Leipzig in the Champions League.
But he will be hoping to that tally on Sunday when his team travel to title rivals Arsenal in the Premier League.