The experienced 36 year-old is a free agent but Evans confirmed that a deal to bring in Bowyer would be out of the budget which the club are working to.
It is now thought Evans will focus his attention on highly rated Torquay midfielder Eunan O'Kane, with a possible club record bid to be lodged to try and land his services.
The Millers had two setbacks yesterday as potential deals for midfielders broke down.