Nelson met Vijayan late last evening in Hyderabad.
This is Nelson's first visit to the country after the new Insurance Act was passed.
IRDA sources confirmed the meeting and said Nelson discussed his organisation's plan to enter the country.
The meeting assumes significance as Lloyd's has already started the process to set up its operations in the country.
Lloyd's needs a separate set of guidelines as unlike several other global reinsurance firms, Lloyd's, set up in 1688, operates not as a company but as a market where multiple members join together as syndicates to reinsure risk.