The former Shakhtar Donetsk and Roma boss has been in contact with the club’s new owners since earlier this summer, though it is understood no final decision has been made regarding the preferred candidate.
Rangers boss Steven Gerrard is among those still under consideration by Newcastle's new owners to replace Steve Bruce, whose tenure at St James’ Park came to an end on Wednesday morning.
Former Bournemouth boss Eddie Howe and ex-Chelsea head coach Frank Lampard are also in the frame, along with Belgium national team manager Roberto Martinez and ex-Borussia Dortmund leader Lucien Favre.
Fonseca has been instilled as the odds-on favourite at the bookies, while Gerrard has drifted out to as much as 20/1 with some oddsmakers.
Bruce's former assistant Graeme Jones will be in charge for Saturday's Premier League trip to Crystal Palace.