The Serbia international spent the second half of last season on loan with the 'Bluebirds', and boss Neil Warnock had expressed his desire to re-sign the player before the end of the transfer window.
Warnock, who has brought in four players already this summer, said "Grujic looks like he will stay put."
"I think he would be better off here, but it is a contract issue. I understand his point of view".
Cardiff City have signed winger Josh Murphy from Norwich and Bobby Reid from Bristol City, as well as goalkeeper Alex Smithies and left-back Greg Cunningham from QPR and Preston respectively.