Stone is currently running at Leeds' Thorp Arch training complex and is expected to step up his efforts over the next week.
The Whites could be given a massive boost with the possible availability of Stone.
Blackwell said in the Yorkshire Evening Post: "Steve has started running again, but I'm putting him under no pressure at all. He hasn't played football for almost a year so it would be wrong of me to expect anything from him.But I've never written him out and if there's a chance there's a chance.
"Stoney has been out for a long, long time and when you've been in that position there are so many conundrums. If he plays it is a big, big bonus, but the last thing I'm going to do is put him under any pressure at all.
"I've not said a lot to the players," added Blackwell, on the recent run of no wins in 5 games.
"They are obviously disappointed because the prize is so great. There are times to be strong and harsh and there are times to stand back and assess it.
"I've got a lot of assessing to do between now and next weekend. I can't fault the effort and when we knocked the ball around we looked a good side.
"But for all the good positions we got ourselves into we kept either firing blanks or lacking imagination."