The 28-year-old turned down the club's offer of a new deal, which will force United to finalise a deal with another club before the summer transfer window shuts at the end of August or risk losing him for nothing.
The Athletic reports the Ligue 1 side have opened initial discussions to "gauge interest" but are yet to submit a formal bid for Pogba.
The report adds that PSG are acting with a sense of caution from a financial point of view, having already completed the free transfers of Sergio Ramos, Gianluigi Donnarumma and Gini Wijnaldum - all of whom will have eaten into the club's wage budget.
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