According to The Sun, Rangers are ready to challenge Newcastle and Manchester United for the Leeds born England international striker.
Ibrox manager Alex McLeish thinks he could get Smith for as little as £4m.
Leeds may be forced to sell Smith along with Mark Viduka if they get relegated.
Middlesbrough and Roma lead the chase for Viduka, 28, who is valued at £9m.
Smith, 23, is on around £40k a week but that has not put Rangers off and McLeish has been given the go-ahead to match Leeds salary and discreet inquiries have already been made about the his availability.