Davis spent the second half of the last campaign on loan at Ibrox, and the Gers are keen to secure the Northern Ireland international on a permanent basis.
But Smith has conceded that Fulham's demands - reportedly in the region of £4million - may price them out of a permanent move for the 23-year-old.
"We've been looking for another midfielder anyway so we have an idea of players who are out there and available," Smith told the Scottish Sun.
"Steve Davis is obviously a player we know, but the money Fulham are talking about is too much for us."