Pedro is attracting interest from MLS clubs New York City FC and Inter Miami after falling out of favour at Chelsea, Goal understands.
The 32-year-old has just six months left on his contract, and is expected to be available on a cut-price deal if Chelsea sanction a move.
With the Blues in the market for another forward, selling Pedro may help them free up space in the squad for more attacking players.
David Beckham's new MLS franchise Inter Miami are trying to attract Pedro by offering a good lifestyle in a city with a large Hispanic population.
Similarly, Manchester City's sister club NYCFC will offer similar benefits having previously attracted Chelsea boss Frank Lampard himself, as well as both David Villa and Andrea Pirlo.
Lampard has only started Pedro six times in all competitions and the Spaniard has made just one start in the last three months.
Pedro has admitted his interest in returning to his previous club Barcelona, although they are not expected to make a move for him in January.
"If Barca call me, I'll drop everything," Pedro told L'Esportiu.
"There was a moment in pre-season when we played against Barca that, after talking with the coach, I saw a chance, but the door closed quickly.
"At this point, I don't know what will happen to me, just that I'm contracted to Chelsea until the end of the season."
Chelsea are yet to state their position to Pedro but he is seriously considering his future away from Stamford Bridge after losing his place to the likes of Christian Pulisic, Willian and Callum Hudson-Odoi.
Olivier Giroud has seen Bordeaux become a serious contender for his signature in January after already having early interest from Inter boss Antonio Conte, whom he previously worked with at Chelsea.
Lyon are also interested but it is unclear whether they will try to sign Valencia's Kevin Gameiro before looking at the France World Cup-winning striker.
Marcos Alonso also has interest from Inter but he will prove expensive for any club wishing to sign him in January due to having a £100,000-a-week contract with the Blues until 2023.
Pedro and Giroud could make way for a new attacker in January with the likes of Dortmund's Jadon Sancho, Crystal Palace's Wilfried Zaha and Villarreal's Samuel Chukwueze among the targets who have been identified.
The club's transfer ban was halved earlier in the month by the Court of Arbitration for Sport (CAS), allowing them to enter the market again following their summer ban imposed by FIFA for wrongdoing in signing minors .
Chelsea are set to sign 16-year-old Norwegian teenager Bryan Fiabema in early January after agreeing a deal with Tromso following a successful trial period.