Rovers want to make an early decision, however, and Dowie could be appointed by the end of the week.
It is understood that a new four-year deal drawn up by Palace chairman Simon Jordan remains unsigned and that Dowie is only contracted to Selhurst Park for another 10 months.
The 39-year old, who made an early impact in his first managerial post at Oldham and continued to prosper by steering Palace into the Premiership, is tempted by the prospect of a return to the North-west, where his wife and children are based.