The micro-blogging platform was barred at the time of mass anti-regime protests in 2009 that followed allegations of massive rigging in the re-election of president Mahmoud Ahmadinejad.
"(Twitter) has announced that it is prepared to negotiate to resolve problems," Mohammad-Javad Azari Jahromi told the Iran daily newspaper.
"Considering the current situation there are grounds for such negotiation and interaction. Twitter is not an immoral environment needing to be blocked," he added.
His selection has been criticised by rights groups over his involvement in surveillance during and after the mass anti-regime protests of 2009.
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He rejected the criticism in a meeting with lawmakers this week, saying: "I wasn't responsible for surveillance -- I was in charge of the technical infrastructure for the surveillance industry, and I consider it an honour."
But Jahromi is also seen as a critic of online censorship in Iran, where platforms like Facebook, YouTube and Twitter remain banned even if millions use them daily through easily available privacy software.
There was no immediate response from Twitter or YouTube.
Jahromi added that the final decision on unblocking sites lay with Supreme Council for Cyberspace, which includes members of the hardline judiciary.
The 2009 protests were considered the first time that Twitter and social media were widely used to organise protests -- a model replicated when the Arab Spring movement erupted across the region the following year.
"At that time and based on remarks made by the director of this network, Iran's government believed they had interfered in the country's internal affairs and for this reason Twitter was filtered," said Jahromi, who has more than 4,000 followers on the service.