Speculation has suggested that Blackstock could be among those on the move during the January transfer window, with Leeds among those said to be keen on acquiring the services of a proven goalscorer.
The fact that his current contract at the City Ground is set to expire at the end of the season has only served to fan the transfer flames.
McLeish is still settling into the managerial hot-seat at Forest, having been drafted in to succeed Sean O'Driscoll, and he acknowledges that he has some 'big decisions' to make - starting with Blackstock and his future on Trentside.
"I am just walking in through the door and am starting to realise we have to make some big decisions very, very quickly," the Scot told the Nottingham Evening Post.
"There is all sorts of speculation about Dexter, but we are not planning to let him go. He is out of contract in the summer and you never know. We will have to see what resources we have available to bring players in.
"But I would hope that Dexter would want to stay the course with us.
"I realise he probably wants a new contract, an extended deal. There are things we have to weigh up."
McLeish is also set to make a decision on the Forest future of Jonathan Greening, with the experienced midfielder having returned to the club from a loan spell at Barnsley.
He added: "Jonathan has been a brilliant player during his career.
"I will have to talk to the staff to decide whether we move forward with him as part of the squad or whether we try and get him back out on loan.
"I know what his qualities are. There was a stage when I really fancied trying to sign him. But now I have him, I have to decide whether he can enhance the squad in the second half of the season."