Taylor, who is out of contract in the summer, remains on the transfer list despite an offer being put on the table.
The ball is now in Taylor's court, because Mike Ashley has given him an improved offer.
Taylor's adviser (the agent who handles Wayne Rooney) rejected the first offer and is yet to respond to the second.
The player has attracted some criticism for his stance by a section of Toon fans who question his loyalty to the club.
The breakdown in talks over the summer were blamed on his agent, who would pick up a tidy sum of money should Taylor leave Newcastle Utd.
The Journal: "Reports have claimed Taylor was asking for as much as £60,000-a-week to sign a new deal, although this has been disputed by his camp.
"Nevertheless, given the Academy graduate is already on an estimated £40,000 a week, it is reasonable to assume he is looking for some sort of increase before he agrees to remain on Tyneside."
Mike Ashley allegedly set a wage cap of £40,000 for new signings, so obviously he has been willing to re-write the rules to accomodate Taylor.