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Mr Trump told presenter Patrick Bet-David in his appearance on the PBD Podcast that Mr Cook had called him a few hours prior to complain about fines the company was forced to pay after breaching EU rules.
He said Mr Cook had told him about a recent $15bn fine from the EU, to which Mr Trump said he responded “that’s a lot”.
“Then on top of that, they got fined by the European Union another $2bn,” Mr Trump continued, “so it’s a $17-18bn fine.”
Apple and the Irish government lost a long-running legal dispute over unpaid taxes in September.
The EU’s highest court upheld an accusation by the bloc’s legislative arm, the European Commission, that Ireland gave Apple illegal tax advantages.
Mr Cook described the Commission’s findings as “political” and said Ireland was being “picked on” in 2016.
The European Commission fined Apple €1.8bn several months earlier in March for allegedly breaking music streaming rules, in a win for rival service Spotify.
According to Mr Trump, the Apple chief executive went on to make a remark about the EU using the money received via antitrust fines to run an “enterprise”.
Antitrust fines paid by firms which breach EU competition rules go towards the bloc’s general budget and “help to finance the EU and reduce the burden for taxpayers,” the Commission’s website states, external.
A Commission spokesperson said antitrust fines are designed to sanction companies that have breached competition rules, as well as deter them and others from engaging in anti-competitive behaviour.
“When determining the amount of the fine, the Commission considers both the gravity and the duration of the infringement,” they told BBC News.
“All companies are welcome in the EU, provided they respect our rules and legislation.”
Mr Trump said he told Mr Cook he would not let the EU “take advantage of our companies”, but he needed to “get elected first”.
The former president has spent some of his campaign trying to woo prominent tech figures, with Tesla and X (formerly Twitter) boss Elon Musk among those backing Mr Trump.
He also said he spoke to Google boss Sundar Pichai earlier this week, and claims to have had multiple calls with Meta boss Mark Zuckerberg in August.
