The hugely-anticipated match is due to be hosted in the northern Indian city of Mohali.
Earlier, Pakistan’s cricket team arrived for their first visit to India since the 2008 Mumbai (Bombay) attacks.
Relations between the nuclear-armed rivals are still tense after Pakistan-based militants targeted the city.
More than 170 people were killed in the attacks, which Pakistan admitted were partly planned on its soil.
The two sides have met a number of times over the past year and Pakistan’s foreign minister was scheduled to visit India by July to discuss the resumption of peace talks.
Formal invitations from Prime Minister Manmohan Singh will be delivered to the Pakistani High Commission for Pakistani President Asif Ali Zardari and Prime Minister Yousuf Raza Gilani, Indian media reports said.
A foreign office spokesman in the Pakistani city of Islamabad said no decision had been made on whether to accept the invitation, the Reuters news agency reported.
Pakistan’s cricket team slipped into India almost unnoticed, despite a frenetic build-up to the match that has already been billed as the ultimate show down, the BBC’s Sanjoy Majumder in Delhi says.
Almost half of the team have never been to India.
Heavy security is already in place for the match but this was stepped up after police said on Thursday they had arrested a man they believed was planning an attack during the World Cup.
Across India and Pakistan there is a mad scramble for tickets for next week’s face-off, our correspondent says.
India has issued 5,000 visas to Pakistanis with confirmed tickets and the government is under pressure to ease restrictions and allow more people in from across the border.
Before the Mumbai attacks, the two sides held formal peace talks known as a “composite dialogue” for several years but made little headway, apart from a number of confidence-building measures.
The main disputes between the two sides centre on counter-terrorism and the Himalayan territory of Kashmir – which both countries claim.
But there are also a number of economic issues and smaller territorial disagreements which divide the sides.
But relations have been slowly improving, although talks ended in acrimony last July with the two sides in a public spat over the disputed territory of Kashmir – BBC