Hodgson admitted there “isn’t any real dialogue” between the two clubs as Palace continue to be linked with the 25-year-old.
Benrahma hit 17 goals last season as Brentford were denied a place in the Premier League after suffering a play-off final defeat to Fulham.
The forward got his first goals of this campaign ironically against Fulham on Thursday, hitting a brace as the Championship outfit beat their top-flight rivals 3-0.
That performance only strengthened the transfer links that have been floating around this window, with Palace regularly tipped to sign Benrahma before the deadline.
But Hodgson played down any move in his pre-Chelsea press conference on Friday.
“Well, once again the name is put out there by somebody,” he said. “I’m in a position where I’ve either got to say ‘No, we’re not interested because the player’s no good’, or ‘Yes we are interested, he’s a good player.’
“But the bottom line is, as far as I’m concerned, there isn’t any real dialogue going on between us and Brentford.
“We certainly haven’t discussed buying a player in his position, of his type.
“But who knows? I’ve got no idea what Brentford are thinking, and it would be very unusual and even stupid of me to come out and say he’s not a good player.
“But we have players in that position. We’ve signed Eze to strengthen us in that area, and on top of that we have Jeffrey Schlupp, Andros Townsend and Max Meyer, so we certainly aren’t short of players in the position in which Said Benrahma plays.”