(I started writing this answer from memory, but on a second look at some sources it turns out to answer the question for the statement of a rotating earth rather than that of a spherical earth... but I'll leave it here; hope the other question is still interesting to you.)
The most notable statement of a spherical rotating earth, in Indian astronomy, is by Āryabhaṭa. In his Āryabhaṭīya (499 CE), he explains the familiar observation of the night sky, of the stars collectively appearing to go around the earth, as being because of the earth's rotation. (He gives the analogy of being in a boat, where things on the shore appear to be moving.)
Āryabhaṭa was always universally revered in the Indian astronomical tradition, and had his followers (especially in Kerala) until pretty much modern times (in the 18th century, the French astronomer Guillaume Le Gentil was in India during a lunar eclipse, and found that the prediction of its length by local astronomers based on Āryabhaṭa's method was more accurate than the European one), but this particular statement about the earth's motion was rejected by many later Indian astronomers (even his own commentators kind of explained it away), because of various physical objections. For example:
And if the earth turns, then how do birds reach their nests again after leaving them? Arrows released up toward the sky should fall down in the west if there is an eastward rotation of the earth, and clouds should move toward the west. Now, if you argue that these effects do not happen because the motion is very slow, then how can the earth complete a full rotation in one day?
In Indian astronomy by this time there were many Greek sources known (starting with the influence of the Indo-Greek kingdoms after the breakup of Alexander's empire); consider works (either available or mentioned) like Pauliśa-siddhānta, Romaka-siddhānta, Yavana-jātaka, etc. Astronomers Varāhamihira and Brahmagupta, both later than Āryabhaṭa, mention these Greek sources and also praise them: “Though the Yavanas [Greeks] are barbarians (mleccha), this science (astronomy) is good among them, and they are revered (pūjyante) like sages — a scholar (div) in these sciences even more so.” However when Brahmagupta criticizes Āryabhaṭa's spinning-earth theory, he does not attribute it to a Greek source.
(I suppose that eventually in a few centuries the rotating earth was widely accepted, or maybe it was not, but in any case it doesn't matter much for the calculations.)
So to summarize, we see that neither Āryabhaṭa nor his commentators nor other astronomers attributed the theory of a rotating earth to Greek astronomy even though they were aware of it, nor was the theory widespread the way (some) ideas from Greek astronomy were, so it seems quite probable that the idea originated in India independently.
Sources: see Kim Plofker's Mathematics in India, the course “Mathematics in India” by M.D.Srinivas, M.S.Sriram and K.Ramasubramanian (I can't find the link to the lecture notes and associated writing, but the videos are here), etc.
(As I said, I realize this is not exactly the question you were asking. The idea of a spherical earth itself (even if possibly fixed instead of rotating) was strongly defended by both Āryabhaṭa's commentators and by other astronomers, and is older than Āryabhaṭa... it was universally preferred in Indian astronomy over any kind of flat earth model.)
