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The source, who declined to be identified, told Reuters that the discussions were in the early stages but could provide no further detail.
TNT declined to comment. A UPS spokesman said on Sunday the company would never discuss rumours or speculation about mergers or acquisitions.
The Sunday Telegraph reported that UPS was planning a 10 billion euros ($15.2 billion) bid for TNT, which has a market value of about 9.6 billion euros.
TNT shares have fluctuated wildly in July and August, first on talk that FedEx had prepared, and then abandoned, a bid. They have traded between 18.49 euros, a four-year-low, and 27.25 euros in the last two months.
Analysts said rivals looking to expand their European operations would be mainly interested in TNT's express delivery unit, which accounts for two-thirds of its sales and is seen as able to ride out any economic downturn.