Blues had a bid for the 31-year-old Scotland international striker accepted by the Ibrox club last week but Miller is still to decide on whether or not he wants to move to St Andrews.
McLeish is keen to tie-up the transfer by 5pm this evening (Friday) which would allow him to include Miller in his squad for the local derby against Aston Villa at St Andrews on Sunday.
"We have not finalised anything. We are still talking to Kenny and his agent,'' McLeish told the Daily Express.
"He has not rejected any offers from any other club and I don't think he will want to commit to anything until he is sure in his own mind what he wants to do.
"I would like to get a definite answer as he would need to be registered by Friday if he could play on Sunday against Aston Villa.
"I am never one who is confident in these matters."I never like to say 'yes' because I have seen so much disappointment in the past."
Italian Serie A side Fiorentina are also keen on signing Miller, who's contract at Rangers expires in the summer.