The Mail reports that Magpies boss Rafael Benitez has become frustrated with the club's inability to find value for money as they continue their preparations for their Championship campaign.
However, he feels that the 25-year-old would tick the boxes and thus, he is seemingly prepared to part with a large of his transfer budget to bring him to St James' Park.
The Mail adds that Gayle only signed a four-year deal with the Eagles in April - which may help explain just why the fee involved in a potential move could be so high - but having struggled to hold down a first-team spot at Selhurst Park, he may feel that dropping down a division to aid Newcastle's promotion bid may be the best way to become a regular in the Premier League.
His record of 15 goals in 64 league games for Palace may not be the most impressive, but becomes a lot more understandable given that he has started just 27 times.
And if United manage to land the forward, and he is able to inspire them towards an instant return to the top flight, then they will certainly reflect that it was money well spent.