The Premier League champions, reeling from their worst start to a season in 17 years, are interested in the Spanish forward.
It is not clear how far negotiations for the 28-year-old have progressed, but United now have a rival for his signature.
Pedro is reportedly available for a fee of £22million.
He would add to Jose Mourinho's attacking options and his potential arrival could lead to a move away from Stamford Bridge for Juan Cuadrado.
Cuadrado, a January arrival from Fiorentina, has struggled to impose himself on the Blues and has been linked with a return to Italy.
Chelsea have one point from their opening two games of the season and are also looking to strengthen in defence.
John Stones has been the subject of a reported three failed bids, with Everton determined to hold on to the England centre back.
The Blues play at West Brom on Sunday and at home to Crystal Palace on Saturday week prior to the closure of the transfer window on Tuesday, September 1, by when Mourinho will hope to have bolstered his options in attack and defence.
Source : PA
Source: PA