The Magpies have already bolstered their defensive options this summer, recruiting Lloyd Kelly on a free transfer following his Bournemouth exit.
However, Newcastle boss Eddie Howe is still keen to bring in another centre-back, with Sven Botman and Jamaal Lascelles both working on their recovery from long-term knee injuries.
Newcastle have identified Guehi as one of their top transfer targets, but they have failed with their first two bids for the England international.
According to BBC Sport, Newcastle are not willing to concede defeat in their pursuit and have now returned to the negotiating table with a third proposal.
The report claims that the third bid is worth around £60m, with the Magpies willing to pay £55m and plus a further £5m in add-ons.
Palace are said to value the England international in the region of £70m so it remains to be seen whether they would be willing to compromise and accept Newcastle's latest offer.
Norton-Cuffy set to leave Arsenal
Meanwhile, Arsenal academy product Brooke Norton-Cuffy is reportedly on the verge of completing a move to Italian side Genoa.
Norton-Cuffy has been unable to force his way into the first-team setup after working his way through Arsenal's academy system.
The 20-year-old spent time on loan with Lincoln, Rotherham United and Coventry City, before he joined Millwall for the full duration of the 2023-24 campaign.
Having experienced four loan spells, the England Under-21 defender is now on the brink of completing a permanent move away from the Emirates Stadium.
According to journalist Fabrizio Romano, Genoa have reached an agreement with Arsenal to sign Norton-Cuffy for €2m (£1.7m) plus add-ons.
Norton Cuffy, who won the Under-19 European Championship with England in 2022, is expected to undergo a medical later this week before he can be unveiled as the latest member of Alberto Gilardino's side.
Zouma's UAE move falls through
Elsewhere, West Ham United defender Kurt Zouma has seen his proposed switch to United Arab Emirates side Shabab Al-Ahli Dubai fall through due to a failed medical.
West Ham are willing to allow Zouma to leave this summer after strengthening their defensive options with the additions of Jean-Clair Todibo and Max Kilman.
Zouma appeared to be on the verge of a West Ham departure, travelling to Dubai with a view to signing a lucrative deal with Shabab Al-Ahli.
However, according to BBC Sport, the proposed transfer has been called off after Zouma failed his medical with the UAE side.
The report claims that the player's advisors are now working to find an alternative club for him to join before the summer transfer window closes.
Zouma, who has less than 12 months left on his contract, has made 103 appearances for the Hammers since joining the club from Chelsea in the summer of 2021.