The Magpies are keen to bolster their options in the centre-back department before the summer transfer window shuts on August 30, and Guehi has emerged as their primary target.
However, Eddie Howe's side have been left frustrated in their negotiations with Palace, who have allegedly rejected four bids four Guehi from the North East outfit.
It is understood that Newcastle's latest offer, allegedly a club-record bid, was deemed 'not enough' by the Eagles, who value Guehi in the region of £65m and remain determined to keep hold of the 24-year-old.
Guehi started as captain for Palace in their 2-1 defeat at Brentford in the Premier League on Sunday, and he has previously stated that he is "relaxed and chilled" over his future.
Newcastle to consider Gomez approach amid Guehi uncertainty?
If Newcastle decide to withdraw their interest in Guehi, then they could turn their attention to another England international in the form of Liverpool's Gomez.
According to the Daily Mail, Newcastle are monitoring Gomez' situation at Anfield ahead of the summer transfer deadline.
The report adds that the Magpies are aware that the 27-year-old is exploring his options after he was left out of Liverpool's matchday squad for last weekend's 2-0 Premier League win at Ipswich Town.
Newcastle are not the only clubs said to be keeping tabs on Gomez, though, as fellow Premier League sides Chelsea, Aston Villa and Fulham, as well as clubs abroad, have all been credited with an interest.
Gomez weighing up Liverpool future
Gomez is the longest serving player within Liverpool current first-team squad after joining the Reds from Charlton Athletic for just £3.5m in 2015.
The versatile defender, who has played at centre-back, right-back and left-back during his time at Anfield, has made a total of 248 appearances for the club across all competitions, winning seven trophies including the Premier League and Champions League.
However, Gomez has struggled to establish himself as a first-team regular for Liverpool, and although he still has three years remaining on his contract, a move elsewhere could appeal to the £45m-rated defender this summer.
Gomez is seemingly behind Virgil van Dijk, Ibrahima Konate and Jarell Quansah in the centre-back pecking order under new boss Arne Slot, while Trent Alexander-Arnold and Andrew Robertson remain Liverpool's first-choice full-backs.