England Under-21 defender Wisdom moved to Pride Park on a season-long loan deal last week, prompting speculation that Hughes could be set for a move to Anfield in the January transfer window.
But Rush insists Wisdom's loan move from Liverpool is purely for football reasons, adding Hughes' position at Derby remains unchanged.
"I think the Andre Wisdom deal was very much as a result of Liverpool's desire for him to come to Derby and further his football education," Rush said.
"Andre was the top of Steve McClaren's list of people he wanted to bring in to strengthen the squad. So no, there is no connection with Will Hughes at all.
"There has been no further movement in terms of Will. From our point of view, we are just looking forward to watching him continue to play for Derby County."
Rush also quashed speculation that Derby have placed a £15million price tag on the player, insisting the club have not placed a value on Hughes.