I cannot find any information on Apple owning treasury stock. Their balance sheet implies they have none. However I assume some may be held through holding companies. Does Apple have any treasury stock at all?
Treasury stock is not really represented in the Balance Sheet as a "Treasury stock" line item in the assets. Some companies will break out Treasury Shares as a line item in the "Shareholders Equity" heading of the balance sheet but Apple hides it in the "Shares Issued and Outstanding" counts under the "Shareholders Equity" heading. As of the most recent Q2 2017 quarterly report There are 5,205,815,000 shares issued against 5,336,166,000 shares outstanding. This indicates that Apple is retaining about 130,351,000 shares in treasury.
On the Q1 10-Q you can see that Apple had 5,255,423,000 shares issued which indicates roughly 49mm shares were repurchased by the end of Q2. You can roughly verify this by looking at page 18 of the Q2 filing in the summary of the share repurchase program. Repurchased as part of an Accelerated Share Repurchase arrangement bleeds between quarters but from February 2017 through May 2017 there have been 17.5mm shares repurchased. 31mm shares were also repurchased on the open market in Q2.
The "shares issued" total is on a downward trend as part of Apple's share repurchase initiative that has been underway for the last couple of years.
Treasury stock = Shares authorized - Shares outstanding. Under a 2021 share repurchase program, Apple repurchased 656 million shares of its own common stock for $85.5 billion (10-K, p46). This is done to support the price which Apple feels best reflects its future growth and profitability (10-K, p17). Apple is authorized to issue 50.4 billion shares and has 16.4 billions shares outstanding, accounting for 33.6 billion treasure shares, up by 550 million net shares from 2020 (10-K, p31).
In Quid's answer, they confused the word "respectively" in the phrase "50,400,000 shares authorized; 16,426,786 and 16,976,763 shares issued and outstanding, respectively" to mean that 16,426,786 was for shares issued and 16,976,763 for shares outstanding. This is not the case; on the face of it there can not be more shares outstanding than issues. The word "respectively" is in reference to the reporting years for the line item on the balance sheet. For Apple's 2021 10-K filing that would be 2021 and 2020.