The Chelsea boss has been reluctant to play Emerson, with Marcos Alonso or Cesar Azpilicueta preferred on the left side of defence.
And Tuttosport claim Emerson views Lampard as a ‘sergeant’, unhappy with the level of control the Blues legend has over his players.
Juventus and Inter Milan are said to be interested in the 25-year-old and are readying bids of up to £28million to secure his return to Serie A.
His agent, Luis Fernando Garcia, recently told Juvenews: ‘We know very well about Juventus’ interest but also about Inter. So far there has been no talk of a transfer with Chelsea, nor has there been any official offer.
“I believe that until May there will be no official offers from the two clubs. In the summer we will decide what to do.”
Emerson has been urged to return to Serie A and stake a claim for Italy’s European Championship squad by national boss Roberto Mancini.
“As for the full-backs, we knew Adam Masina, although he disappeared from the radar a bit after his move to Watford,” Mancini told Gazzetta dello Sport.
“Luca Pellegrini [the Cagliari full-back on loan from Juventus] already spent time with the senior squad and can improve.
“It would be nice if Emerson Palmieri, who hasn’t played much for Chelsea, could come and play in Italy.”