You can’t use reinterpret because a BigInt is stored as a pointer and some lengths, but you can get at the raw bytes in a variety of ways, from low-level (exploit the raw pointer) to high-level. The best-documented way is to use the digits! function:
julia> a = big(11)^100
137806123398222701841183371720896367762643312000384664331464775521549852095523076769401159497458526446001
jjulia> digits!(Vector{UInt8}(undef, ndigits(a; base=256)), a, base=256)
44-element Vector{UInt8}:
0xb1
0xe1
0x4f
0x64
0xe2
0x52
0xe1
⋮
0xcc
0xf1
0x0e
0x71
0xd8
0x03
See also the discussion in BigInt to bytes — since that discussion, digits! got optimized using mpz_export as explained in the thread.
What are you trying to accomplish?