Dobbins, who flew in from Kabul, will meet Sharif and "brief us on developments relating to Afghanistan," foreign ministry spokesman, Aizaz Ahmad Chaudhry told AFP.
Other Pakistani officials said the meetings of Dobbins, the US special representative to Afghanistan and Pakistan, will focus on "efforts to promote an Afghan-led reconciliation process".
The Afghan Taliban opened an office in Qatar last Tuesday in a step towards talks as the US-led NATO combat mission prepares to leave Afghanistan in 2014 despite a resilient Taliban insurgency 12 years after they were ousted following the 9/11 attacks.
Kabul, which says it is committed to the peace process, insisted that the Qatar office be used for only direct negotiations between the Taliban and the Afghan government.
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Pakistani Taliban spokesman Ehsanullah Ehsan in a video released to media said the insurgents will follow any decision taken by Afghan Taliban leader Mullah Omar.
"Mullah Omar is our Amir (chief) and we will abide by any decision he takes regarding peace talks with America," Ehsan said.
Some experts have suggested that Pakistan likely played a key role in persuading a reluctant Taliban to consider tentative peace talks with its American and Afghan government foes.
Western capitals believe that Pakistan can play a crucial role in helping to get the Taliban to the negotiating table as it was one of only three countries to recognise its 1996-2001 regime in Kabul.