"Who said to US Cong on 13/3/13 the US should act against India to defend US Pharmaceuticals interests? Arvind Subramanian MoF !! Sack him!!!," he tweeted.
Swamy's attack comes in the wake of reports of Arvind Subramanian being among the probable successors of Rajan as the country's central bank chief.
"Guess who encouraged Congi to become rigid on GST clauses? Jaitley's economic adviser Arvind Subramanian of Washington DC," Swamy tweeted, saying he is "helping Jaitely to recognise the enemies in our camp".
"Was AS (Arvind Subramanian) deposing before US Cong Committee against India as a US citizen or Indian? Does any PT know?," he asked.
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"Subramanian Swamy now guns for Arvind Subramanian Economic Advisor to NDA. Target is Arun Jaitley not Arvind Subramanian.
"He has been claiming that PM has assured him as quid pro quo if he targeted Nehru Gandhi Family," Singh said in a series of tweets.
Swamy had earlier launched a scathing attack on Rajan, who announced last week that he would return to academics after his current tenure as RBI Governor ends on September 4.
Swamy had attacked Rajan, saying he is 'unfit' for the job and is 'mentally not fully Indian'.
Incidently, both Rajan and Arvind Subramanian have worked at the IMF.
While Rajan was a UPA appointee, Arvind Subramanian was appointed by the Narendra Modi government.