According to Gazzetta dello Sport, Chelsea's interest in the Portugal international has been revived this summer, with a serious approach now dependent on Neto completing a move to Saudi Arabian club Al-Hilal.
Neto has been strongly linked with the Riyadh side in the closing stages of the window, and Chelsea are said to view Conceição as a ready-made replacement on the right flank should that sale go through.
The 23-year-old has previously been linked with both Liverpool and Manchester United during the summer, though neither move advanced significantly.
The two clubs are understood to be some way apart on valuation. Chelsea's opening offer is reported to be in the region of €30million, while Juventus want closer to €40million before sanctioning a sale — a gap Chelsea may need to bridge if they are to complete the deal before deadline day.
Juventus paid an initial fee plus a subsequent obligation to buy worth €41.5million in total to sign Conceição from Porto, having first taken him on loan.
Conceição has made 82 competitive appearances for Juventus, scoring 11 goals and providing 11 assists, and has become a regular feature of Luciano Spalletti's plans since his move to Turin. He has also earned 21 caps for Portugal, scoring four goals, and remains under contract in Turin until the summer of 2030 regardless of how the current speculation unfolds.
Whether the move materialises is likely to depend heavily on developments elsewhere.
Chelsea's willingness to pursue Conceição is explicitly tied to Pedro Neto's own exit, meaning the winger's future may be decided as much by events in west London and Riyadh as by anything happening at Juventus' Continassa training base.
For Juventus, the situation adds an unwelcome complication to the closing days of the window.
Reports from Turin suggest Conceição himself would prefer to stay and continue his development under Spalletti, viewing the club as the right environment for his career at this stage, but Juventus may ultimately have limited room to resist an offer that meets their valuation if it materialises before the deadline.