The Millers have been in discussions regarding new terms with the 22-year-old, whose current deal expires in the summer, since early in the season and manager Ronnie Moore hopes to get it sorted before the visit of Southend on Saturday.
"We're very close to doing a deal with him for two-and-a-half years and it would be nice if we can do that before the weekend," Moore told Press Association Sport.
"It's great when a local home-grown kid comes through and performs like he is doing and long may that continue.
"He wants to stay and I am sure that will be done before the weekend."
The new deal would be a timely boost for the Millers, with Taylor in fine recent form, having scored four goals in the last five games.