Rumours were widespread that the home-grown star was on his way out of The Riverside.
Parnaby, 22, was targeted by Fulham earlier this month - but Boro are believed to have rebuffed that enquiry.
Danny Mills - on loan from Leeds - is first choice right back at the club and if he completes a permanent switch then Parnaby knows his chances will become limited.
He is versatile and played left back against Arsenal in the FA Cup and Boro do hold him in high regard, but his lack of first-team football could place a question mark over his future.
However, McClaren has denied that any offer has been made for him.
"It is complete rubbish to say that any bid has been made," he told skysports.com.
"There has been no such offer for Stuart and he is in the squad for the Leeds game."
