Hereford players Mike McGrath and Alex Harris have both turned down approaches during November.
McGrath was approached by his former manager Richard Sneekes, who is now at Sutton Coldfield. The pair had previously been together at Rushall Olympic.
Meanwhile a club from the Southern League South and West, and his previous club Cinderford Town, both showed interest in goalkeeper Harris. The Foresters are currently bottom of the Southern Premier and without a win since August.
*Update 23/11/16 10:52 - Cinderford beat Chippenham 3-2 last night (Tuesday).
*Update 23/11/16 10:52 - Cinderford beat Chippenham 3-2 last night (Tuesday).
"Both players have a superb attitude and believe in the way we do things here," Hereford manager Pete Beadle told the OS.
"A lot of players have already left this season and I truly believe that it was because they couldn’t play under the expectation and demands of this football club.
"We have high standards here and we are not your average Non League club. It takes a special type of player to succeed at Hereford FC.
"Some players are happy just to play in their comfort zone and not test themselves, when you come here you have to be at your very best every time you step on the training pitch and every match day. That in itself can be a daunting and scary prospect."
Beadle's comments in full can be read here (link).