The Polish striker has been in red-hot form for Serie A club Genoa this season, scoring seven goals in as many games.
Piatek has been placed at the top of Sarri’s wanted list, but they face stiff competition from a host of clubs, including Juventus, Bayern Munich and Barcelona.
Other stories from 14th October’s Sunday Mirror:
Eden Hazard must quit Chelsea to reach the top says former Blues star Boudewijn Zenden
Rafa Benitez fears Newcastle sack before end of season – to save Mike Ashley from anger of fans
Aaron Ramsey transfer: Manchester United plot THIRD move for Arsenal star after failed approach last summer
Sergio Ramos admits the chance to give England a kicking is always a thrill
Jordan Henderson reveals the difference between no-nonsense Jurgen Klopp and Gareth Southgate
Manchester United ‘in contact with Massimiliano Allegri as Red Devils look for Jose Mourinho replacement’