Director of football Gordon Smith has been in talks with the La Liga club over a move for the 23-year-old.
"We've spoken to Espanyol and we'll speak to them again to try to come to an agreement over a fee," Smith told BBC Scotland.
"They've given us an idea of what they're looking for, so hopefully we can get something done."
Rodriguez has made 10 first-team appearances for the Barcelona club after breaking into the team last season.
Another Spaniard, former Almeria winger Juan Manuel Ortiz, has been the Ibrox club's only summer signing so far.