Modi conveyed this wish of his to President Pranab Mukherjee when he met him on Tuesday.
The President seemingly welcomed it as a 'good idea' and has passed this on to the ministry of external affairs which is now examining the proposal, sources in Rastrapati Bhavan said here.
There is no recent precedent for inviting foreign heads of governments when an Indian prime minister has been sworn in, but Modi has a penchant for doing the most unusual.
SAARC nations include Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, Sri Lanka and Afghanistan.
Modi apparently wants to send out through this invitation a "very strong signal of a neighbour-friendly new government ", BJP sources say.