The investigation into possible "planned obsolescence" or "fraud" was opened on Friday and is being led by anti-trust and consumer protection specialists in the French economy ministry, the source said.
At the end of past year, Apple apologised for deliberately slowing down some ageing iPhone models via software updates but said it did so in order to prolong battery life and not to force customers to upgrade.
Paris prosecutors have launched a probe of USA tech giant Apple over suspected "planned obsolescence" in some of its iPhone models, a judicial source told AFP on Monday.
A French prosecutor has launched a formal investigation into claims Apple deliberately slowed older iPhones.
France has notoriously strict laws against planned Obsolescence, Reuters says that companies found guilty of "shortening the life of their products to spur demand to replace them" risk fines of up to 5 percent of their annual sales.
In other news, Apple on Monday released an updated version of its operating system software to fix a major microchip security flaw that affected almost all computer chips made in the last decade.
Apple, naturally, hasn't commented, but instead pointed to a statement made on 28 December in which it "apologised" for its handling of the throttling issue.
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Mourinho is a big fan of the player, who has been a key member of his squad, so the news may come as a surprise to some fans.
"First and foremost, we have never - and would never - do anything to intentionally shorten the life of any Apple product, or degrade the user experience to drive customer upgrades", said Apple.
A French consumer association called "HOP" - standing for "Stop Planned Obsolescence" - filed a legal complaint against Apple.
Meaningful developments in the investigation may take a long time.
Reuters reported the preliminary investigation could take a number of months and will either be dropped or passed on to a judge for further investigation, depending on the findings.
France won't be the only country looking for answers from the Cupertino tech giant.
By including a patch that makes older iPhones perform worse without telling consumers, the group pointed out that it could be considered a move by Apple to force customers to upgrade to new phones.