Defender Mike Edwards and influential midfielder Gavin Mahon join youngsters Liam Mitchell and Haydn Hollis in being offered new terms and all four have until Friday, May 25 to put pen to paper.
Meanwhile, 13 players have been told that they will not be offered new contracts this summer, including goalkeeper Stuart Nelson, defenders Stephen Hunt, Sam Sodje and Liam Chilvers and strikers Karl Hawley and Ben Burgess.
On a busy day of one-to-one meetings with his playing staff, Curle also told defender Krystian Pearce that he was to be made available for transfer this summer.
Striker Lee Hughes was unable to meet with the manager on Wednesday due to personal circumstances but he will be sitting down with Curle later in the week.
Youth team players Fabian Spiess, Jake Wholey and Greg Tempest have all accepted professional deals.