The same article states that the Europa League winners are interested in signing the Poland international from Serie A side Napoli.
However, Manchester United are expected to face competition from their bitter city rivals Manchester City.
Pep Guardiola is already thought to have submitted an enquiry about the Polish star to Napoli as the Citizens boss looks to continue his summer splurge.
According to Transfer Market Web, Arsenal, Bayern Munich, Paris Saint-Germain and Real Madrid are all interested in Zielinski – too.
Manchester United signed Serbia international Nemanja Matic in a £40m deal from Premier League champions Chelsea on Monday evening.
Matic is the third summer arrival at Old Trafford after Manchester United signed Sweden international Victor Lindelof in a £30.7m deal from Portuguese champions Benfica.
The Red Devils have also signed Romelu Lukaku in a £75m deal from Everton to see off interest from Chelsea in re-signing the Belgian striker.
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