There is some data like that, but not split by private/government entities holding it.
Exhibit 5 compares foreign holdings of U.S. long-term securities with estimates of U.S.
holdings of foreign long-term securities as of selected survey dates. At \$17,481 billion, foreign
holdings of U.S. long-term securities remained considerably larger than the \$10,734 billion in
foreign securities held by U.S. residents at end-June 2017.
Actually BEA has more up-to-date NIIP data. The latter includes much more than just long-term securities, e.g. derivatives too.
The US Fed does buy some foreign currencies as part of their SOMA (System
Open Market Account) operations, and the Treasury also does that through their Exchange Stabilization Fund (ESF). According to that source these
are held in [...] in a variety of instruments that yield market rates of return in their respective currencies and have a high degree of liquidity and credit quality.
As of June 30 , the euro reserves held by both the SOMA and the ESF totaled \$25.4 billion [...] The amount of yen-denominated deposits and government securities held by the SOMA and the ESF fell to \$16.9 billion [...].
Note that these numbers are pretty insignificant relative to the private positions from the first graph I posted.
The same source mentions that the US does have reciprocal currency swaps with the ECB and the BoJ (about \$1 billion with each). It doesn't have any with China though and the latter's central bank holds large US reserves, trillions...