An official response from the US is still awaited.
However, in the past few weeks, Washington is said to have indicated to New Delhi that the Trump administration is favourably considering the invite, the daily reported. The invite was sent in April and followed up by several rounds of diplomatic engagement.
The invitation by the Narendra Modi government comes amid difference with the US over trade tariffs and the latter's sanctions on Iran.
Trump's predecessor, Barack Obama, was the chief guest for the 2015 Republic Day parade and celebrations.
Leaders of all the 10 countries of the ASEAN bloc were the chief guests for the 2018 parade.