The Cameroon midfielder enjoyed a very successful loan spell on Teesside last season and Boro were looking to seal a permanent deal.
Real set a fee of just over £9 million, which Boro were not willing to pay.
Talks have been deadlocked in recent weeks, but McClaren still holds out some hope of landing the African.
"If at all possible we would like to bring him here," McClaren told Skysports.
"But at this moment it does not look possible."
The Boro boss is, though, more confident about the future of Celta Vigo's Doriva - who also spent time on loan at The Riverside during the last campaign.
"He has acclimatised very well, which was always going to be a doubt," McClaren continued.
"He is the type of player we are trying to bring here, he had a great season with us."
