Taylor, 23, has reportedly passed a medical at Bramall Lane after the two clubs agreed an undisclosed fee and is now in talks with the Blades over personal terms.
Barnes told the Liverpool Echo: "We're hoping that a fee for Taylor will help us with the budget because we are working with much less than last season.
"Maybe we can bring in more players. We certainly can't afford to bring in someone who is going to cost more than Andy Taylor, but we will try to bring in one or two more players."
The Blades' move for Taylor, who made 81 first-team appearances for Tranmere after signing from home-town club Blackburn 18 months ago, would appear to signal their resignation of losing star defender Kyle Naughton, who is the subject of formal offers from Everton last week and latterly Tottenham.
It is understood Tottenham and now Everton have made bids for both Naughton and fellow Blades defender Kyle Walker, with the latter expected to be loaned back to the South Yorkshire club for another year.