The deal would still have left the 21-year-old defender among the lowest earners at St James's Park.
"I only hope that they are not trying to force Steven out," Alf said. "He loves Newcastle United, and it's the only club he wants to play for, but he's disappointed at what they are offering him."
Taylor - whose basic wage is less than a third of the £30,000 new signing Abdoulaye Faye is understood to be picking up at United - is aware of how much the likes of Milner are being paid in their new contracts.
The former Monkseaton High School pupil has two years left to run on his current deal, which was signed before he became a first-team regular.
Taylor has made 90 appearances for The Toon and was called into the full England squad for last month's friendly against Germany at Wembley.