Any quickening of the endgame in Afghanistan is a concern for India, which fears a US withdrawal would leave it exposed to an unfriendly, Pakistan-dominated neighbourhood and unfettered militancy in its backyard.
The trip will be Singh's first visit to Afghanistan since 2005 and comes just over a week after bin Laden was killed by US special forces in Pakistan.
The official, who spoke on condition of anonymity and declined to provide an exact date for the visit, said India was interested in hearing Afghan President Hamid Karzai's views on the killing of bin Laden.
"Obviously, the situation post the killing of bin Laden is of concern to all of us, and we would like to hear what Mr Karzai has to say," the official told reporters.
"The Taliban groups which have sanctuary in Pakistan, I don't believe they stand diminished (by bin Laden's death). The groups seem as strong and virulent as ever. The threat has not gone away."
Nuclear-armed rivals India and Pakistan, which have gone to war three times since 1947, have for decades sought to secure leverage in the country, which gained urgency after US President Barack Obama announced a tentative timeline to start withdrawing military forces from July.
India is Afghanistan's biggest regional aid donor and sixth largest overall. It has pledged $1.3 billion of projects, from building a parliament to a highway to Iran to establish what officials in New Delhi like to term "soft power".
Pakistan derides those attempts to secure influence in what it considers its neighbourhood, but Islamabad has been concerned by a succession of governments in Kabul that it sees as too cosy with New Delhi.
India's embassy in Kabul was hit by two bomb attacks in 2008 and 2009, killing 75 people and wounding hundreds.
The Taliban claimed responsibility for the blasts, but India has blamed Pakistan's military spy agency, the ISI, for attacks on Indians in Afghanistan to undermine New Delhi's influence.